Question

Find the square root of:

$\left(i\right)\frac{441}{961}$ $\left(ii\right)\frac{324}{841}$ $\left(iii\right)4\frac{29}{49}$ $\left(iv\right)2\frac{14}{25}$ $\left(v\right)2\frac{137}{196}$

$\left(vi\right)23\frac{26}{121}$ $\left(vii\right)25\frac{544}{729}$ $\left(viii\right)75\frac{46}{49}$ $\left(ix\right)3\frac{942}{2209}$ $\left(x\right)3\frac{334}{3025}$

$\left(xi\right)21\frac{2797}{3364}$ $\left(xii\right)38\frac{11}{25}$ $\left(xiii\right)23\frac{394}{729}$ $\left(xiv\right)21\frac{51}{169}$ $\left(xv\right)10\frac{151}{169}$

Answer 1

$\left(i\right)\sqrt{\frac{441}{961}}=\sqrt{\frac{441}{961}}$

$=\frac{21}{31}$

$\left(ii\right)\sqrt{\frac{324}{841}}=\sqrt{\frac{324}{841}}$

$=\frac{18}{29}$

$\left(iii\right)\sqrt{4\frac{29}{49}}=\sqrt{\frac{4\times 49+29}{49}}$

$=\sqrt{\frac{196+29}{49}}=\sqrt{\frac{225}{49}}$

$=\frac{15}{7}=2\frac{1}{7}$

$\left(iv\right)\sqrt{2\frac{14}{25}}=\sqrt{\frac{2\times 25+14}{25}}$

$=\sqrt{\frac{64}{25}}=\frac{\sqrt{64}}{\sqrt{25}}=\frac{8}{5}=1\frac{3}{5}$

$\left(v\right)\sqrt{2\frac{137}{196}}=\sqrt{\frac{2\times 196+137}{196}}$

$=\sqrt{\frac{392+137}{196}}=\sqrt{\frac{529}{196}}$

$=\frac{\sqrt{529}}{\sqrt{196}}$

$=\frac{23}{14}=1\frac{9}{14}$

$\left(vi\right)\sqrt{23\frac{26}{121}}=\sqrt{\frac{23\times 121+26}{121}}=\sqrt{\frac{2783}{121}}$

$=\frac{2809}{121}$

$=\frac{53}{11}=4\frac{9}{11}$

$\left(vii\right)\sqrt{25\frac{544}{729}}=\sqrt{\frac{25\times 729+544}{729}}$

$=\sqrt{\frac{18225+544}{729}}=\sqrt{\frac{18769}{729}}$

$=\frac{137}{27}=5\frac{2}{27}$

$\left(viii\right)\sqrt{75\frac{46}{49}}=\sqrt{\frac{75\times 49+46}{49}}$

$=\sqrt{\frac{3675+46}{49}}=\sqrt{\frac{3721}{49}}$

$=\frac{61}{7}=8\frac{5}{7}$

$\left(ix\right)\sqrt{3\frac{942}{2209}}=\sqrt{\frac{3\times 2209+942}{2209}}$

$=\sqrt{\frac{6627+942}{2209}}=\sqrt{\frac{7569}{2209}}$

$=\frac{87}{47}=1\frac{40}{47}$

$\left(x\right)\sqrt{3\frac{334}{3025}}=\sqrt{\frac{3\times 3025+334}{3025}}$

$=\sqrt{\frac{9075+334}{3025}}=\sqrt{\frac{9409}{3025}}$

$=\frac{97}{55}=1\frac{42}{55}$

$\left(xi\right)\sqrt{21\frac{2797}{3364}}=\sqrt{\frac{21\times 3364+2797}{3364}}$

$=\sqrt{\frac{70644+2797}{3364}}=\sqrt{\frac{73441}{3364}}$

$=\frac{271}{58}=4\frac{39}{58}$

$\left(xii\right)\sqrt{38\frac{11}{25}}=\sqrt{\frac{38\times 25+11}{25}}$

$=\sqrt{\frac{950+11}{25}}=\sqrt{\frac{961}{25}}$

$=\frac{31}{5}=6\frac{1}{5}$

$\left(xiii\right)\sqrt{23\frac{394}{729}}=\sqrt{\frac{23\times 729+394}{729}}$

$=\sqrt{\frac{16767+394}{729}}=\sqrt{\frac{17161}{729}}$

$=\frac{131}{27}=4\frac{23}{27}$

$\left(xiv\right)\sqrt{21\frac{51}{169}}=\sqrt{\frac{21\times 169+51}{169}}$

$=\sqrt{\frac{3549+51}{169}}=\sqrt{\frac{3600}{169}}$

$=\frac{60}{13}=4\frac{8}{13}$

$\left(xv\right)\sqrt{10\frac{151}{225}}=\sqrt{\frac{10\times 225+151}{225}}$

$=\sqrt{\frac{2250+151}{225}}=\sqrt{\frac{2401}{225}}$

$=\frac{49}{15}=3\frac{4}{15}$