https://peda.net/id/050ccee6c22 2018-09-27T10:36:17+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/a2d7b58ac70 2018-10-03T14:51:17+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B48%7D%3D%5Csqrt%7B4%7D%5Csqrt%7B4%7D%5Csqrt%7B6%7D%3D4%5Csqrt%7B6%7D" alt="\sqrt{48}=\sqrt{4}\sqrt{4}\sqrt{6}=4\sqrt{6}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cfrac%7B4%7D%7B81%7D%7D%3D%5Cfrac%7B2%7D%7B9%7D" alt="\sqrt{\frac{4}{81}}=\frac{2}{9}"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B5%7D%2B%5Csqrt%7B20%7D%3D%5Csqrt%7B5%7D%2B%5Csqrt%7B4%7D%5Csqrt%7B5%7D%3D%5Csqrt%7B5%7D%2B2%5Csqrt%7B5%7D%3D3%5Csqrt%7B5%7D" alt="\sqrt{5}+\sqrt{20}=\sqrt{5}+\sqrt{4}\sqrt{5}=\sqrt{5}+2\sqrt{5}=3\sqrt{5}"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B5%2B20%7D%3D%5Csqrt%7B25%7D%3D5" alt="\sqrt{5+20}=\sqrt{25}=5"/><br/> e)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B3%7D%2B%5Csqrt%7B3%7D%3D2%5Csqrt%7B3%7D" alt="\sqrt{3}+\sqrt{3}=2\sqrt{3}"/><br/> f)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B3%7D%5Ccdot%5Csqrt%7B3%7D%3D%5Cleft(%5Csqrt%7B3%7D%5Cright)%5E2%3D%5Csqrt%7B9%7D%3D3" alt="\sqrt{3}\cdot\sqrt{3}=\left(\sqrt{3}\right)^2=\sqrt{9}=3"/><br/> g)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B3%7D%5Ccdot%5Csqrt%7B12%7D%3D%5Csqrt%7B3%7D%5Ccdot%5Csqrt%7B3%7D%5Ccdot%5Csqrt%7B4%7D%3D2%5Cleft(%5Csqrt%7B3%7D%5Cright)%5E2%3D2%5Csqrt%7B9%7D%3D2%5Ccdot3%3D6" alt="\sqrt{3}\cdot\sqrt{12}=\sqrt{3}\cdot\sqrt{3}\cdot\sqrt{4}=2\left(\sqrt{3}\right)^2=2\sqrt{9}=2\cdot3=6"/><br/> h)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B3%7D%2B%5Csqrt%7B12%7D%3D%5Csqrt%7B3%7D%2B2%5Csqrt%7B3%7D%3D3%5Csqrt%7B3%7D" alt="\sqrt{3}+\sqrt{12}=\sqrt{3}+2\sqrt{3}=3\sqrt{3}"/> 2018-10-03T14:51:17+03:00 https://peda.net/id/56197e7ac6f 2018-10-03T14:27:39+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%7Ba%7D%7D%7B%5Csqrt%7Bb%7D%7D" alt="\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a%5Cge0%5C%20b%3E0" alt="a\ge0\ b&gt;0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=k%C3%A4ytet%C3%A4%C3%A4n%5C%20laskus%C3%A4%C3%A4nt%C3%B6%C3%A4%5C%20koska%5C%20b%5Cne0" alt="käytetään\ laskusääntöä\ koska\ b\ne0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%7Ba%7D%7D%7B%5Csqrt%7Bb%7D%7D" alt="\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}"/> 2018-10-03T14:27:39+03:00 https://peda.net/id/8a6ad0dcc6f 2018-10-03T14:07:46+03:00 a) c&lt;1<br/> b) c=1 2018-10-03T14:07:39+03:00 https://peda.net/id/05627c3cc6f 2018-10-03T14:03:55+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B5%7D%7Bx%7D%3D%5Cfrac%7Bx%7D%7B20%7D" alt="\frac{5}{x}=\frac{x}{20}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=100%3Dx%5E2" alt="100=x^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=10%3Dx" alt="10=x"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%7D%7B6%7D%3D%5Cfrac%7B3%7D%7B2x%7D" alt="\frac{x}{6}=\frac{3}{2x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%3D18" alt="2x^2=18"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D9" alt="x^2=9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><!--filtered attribute: style="display: inline;"--><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7Bx%2B1%7D%7Bx%2B6%7D%3D%5Cfrac%7B1%7D%7Bx%7D" alt="\frac{x+1}{x+6}=\frac{1}{x}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(x%2B1%5Cright)%3D1%5Cleft(x%2B6%5Cright)" alt="x\left(x+1\right)=1\left(x+6\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2Bx%3Dx%2B6" alt="x^2+x=x+6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3Dx-x%2B6" alt="x^2=x-x+6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D6" alt="x^2=6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%7B6%7D" alt="x=\sqrt{6}"/> 2018-10-03T14:03:55+03:00 https://peda.net/id/e9ed0d24c6f 2018-10-03T13:56:00+03:00 a) koska se on negatiivinen, eikä neliöjuuri voi olla negatiivinen<br/> b) ei, koska se on negatiivinen 2018-10-03T13:56:00+03:00 https://peda.net/id/96a0d2c2c6f 2018-10-03T13:53:40+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%3D%5C%20%5Csqrt%7B9%7D%7B%2C%7D%5C%20%5Csqrt%7B7%7D%7B%2C%7D%5C%20%5Csqrt%7B8%7D" alt="3=\ \sqrt{9}{,}\ \sqrt{7}{,}\ \sqrt{8}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B7%7D%7B%2C%7D%5C%20%5Csqrt%7B8%7D%7B%2C%7D%5C%203" alt="\sqrt{7}{,}\ \sqrt{8}{,}\ 3"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B7%7Don%5C%20piste%5C%20F%7B%2C%7D%5C%20koska%5C%20se%5C%20on%5C%202%5C%20ja%5C%203%5C%20v%C3%A4liss%C3%A4" alt="\sqrt{7}on\ piste\ F{,}\ koska\ se\ on\ 2\ ja\ 3\ välissä"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7Don%5C%20piste%5C%20D%5C%20koska%5C%20se%5C%20on%5C%200%5C%20ja%5C%201%5C%20v%C3%A4liss%C3%A4" alt="\frac{1}{\sqrt{2}}on\ piste\ D\ koska\ se\ on\ 0\ ja\ 1\ välissä"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-%5Csqrt%7B5%7Don%5C%20piste%5C%20B%5C%20koska%5C%20se%5C%20on%5C%20-2%5C%20ja%5C%20-3%5C%20v%C3%A4liss%C3%A4" alt="-\sqrt{5}on\ piste\ B\ koska\ se\ on\ -2\ ja\ -3\ välissä"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-%5C%20%5Csqrt%7B10%7Don%5C%20piste%5C%20A%7B%2C%7D%5C%20koska%5C%20se%5C%20on%5C%20-3%5C%20ja%5C%20-4%5C%20v%C3%A4liss%C3%A4" alt="-\ \sqrt{10}on\ piste\ A{,}\ koska\ se\ on\ -3\ ja\ -4\ välissä"/> 2018-10-03T13:53:40+03:00 https://peda.net/id/62852bfac23 2018-09-27T11:43:19+03:00 a)<br/> 7^2=49<br/> b)<br/> 6<br/> c)<br/> 20 2018-09-27T11:43:19+03:00 https://peda.net/id/a55be064c23 2018-09-27T11:40:23+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=9x%5E2%3D4" alt="9x^2=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D%5Cfrac%7B4%7D%7B9%7D" alt="x^2=\frac{4}{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Cfrac%7B2%7D%7B3%7D" alt="x=\pm\frac{2}{3}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=100x%5E2-4%3D0" alt="100x^2-4=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=100x%5E2%3D4" alt="100x^2=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D%5Cfrac%7B4%7D%7B100%7D" alt="x^2=\frac{4}{100}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Cfrac%7B2%7D%7B10%7D" alt="x=\pm\frac{2}{10}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Cfrac%7B1%7D%7B5%7D" alt="x=\pm\frac{1}{5}"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B25%3D9" alt="x^2+25=9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D-16" alt="x^2=-16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%7B-16%7D" alt="x=\sqrt{-16}"/><br/> ei voi ratkaista<br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2-80%3D0" alt="2x^2-80=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D40" alt="x^2=40"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%7B2%5Ccdot2%5Ccdot2%5Ccdot5%7D" alt="x=\sqrt{2\cdot2\cdot2\cdot5}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%7B4%7D%5Csqrt%7B10%7D" alt="x=\sqrt{4}\sqrt{10}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm2%5Csqrt%7B10%7D" alt="x=\pm2\sqrt{10}"/><br/> e)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D100x" alt="x^2=100x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D100" alt="x=100"/><br/> f)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B2%7D%7B3%7Dx%5E2-%5Cfrac%7B3%7D%7B2%7D%3D0" alt="\frac{2}{3}x^2-\frac{3}{2}=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B2%7D%7B3%7Dx%5E2%3D%5Cfrac%7B3%7D%7B2%7D" alt="\frac{2}{3}x^2=\frac{3}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D%5Cfrac%7B2%7D%7B3%7D%5Ccdot%5Cfrac%7B2%7D%7B3%7D" alt="x^2=\frac{2}{3}\cdot\frac{2}{3}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D%5Cfrac%7B4%7D%7B9%7D" alt="x^2=\frac{4}{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Cfrac%7B2%7D%7B3%7D" alt="x=\pm\frac{2}{3}"/> 2018-09-27T11:38:02+03:00 https://peda.net/id/1d72847ac22 2018-09-27T11:19:55+03:00 a) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B2%5E2%7D%3C%5Csqrt%7B7%7D%3C%5Csqrt%7B3%5E2%7D" alt="\sqrt{2^2}&lt;\sqrt{7}&lt;\sqrt{3^2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B4%7D%3C%5Csqrt%7B7%7D%3C%5Csqrt%7B9%7D" alt="\sqrt{4}&lt;\sqrt{7}&lt;\sqrt{9}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(%5Csqrt%7B2%7D%5Cright)%5E3%3C%5Cleft(%5Csqrt%7B3%7D%5Cright)%5E2" alt="\left(\sqrt{2}\right)^3&lt;\left(\sqrt{3}\right)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B8%7D%3C%5Csqrt%7B9%7D" alt="\sqrt{8}&lt;\sqrt{9}"/> 2018-09-27T11:19:55+03:00 https://peda.net/id/65eadc4ec22 2018-09-27T11:14:47+03:00 a) epätosi, 0 ei voi olla neliönsä neliöjuuri<br/> b) tosi, koska <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7Ba%5E2%7D%3Da" alt="\sqrt{a^2}=a"/> 2018-09-27T11:14:47+03:00 https://peda.net/id/ec40cbdec22 2018-09-27T11:05:31+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D100" alt="x^2=100"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm10" alt="x=\pm10"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-25%3D0" alt="x^2-25=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D25" alt="x^2=25"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm5" alt="x=\pm5"/><!--filtered attribute: style="display: inline;"--><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%5E2-12%3D0" alt="3x^2-12=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%5E2%3D12" alt="3x^2=12"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D4" alt="x^2=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm2" alt="x=\pm2"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%5E2%2B13%3D0" alt="-x^2+13=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D13" alt="x^2=13"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Csqrt%7B13%7D" alt="x=\sqrt{13}"/> 2018-09-27T11:04:13+03:00