Practice: Taking The Square Root Of Fractions

Simplify this to get- $\sqrt{ \frac {9}{4}} + \sqrt{ \frac {25}{9}}$ $\Rightarrow \frac{3}{2} + \frac{5}{3}$ $\Rightarrow \frac{9 + 10}{6}$ $\Rightarrow \frac{19}{6}$

From here, we get $a = 19$ and $b = 6$ . Hence $a + b = 19 + 6 = \fbox{25}$ .

First, we see that $2 \frac{1}{4}=\frac{9}{4}$ , so the square root of $2 \frac{1}{4}$ is $\frac{3}{2}$ . We also see that $2 \frac{7}{9}=\frac{25}{9}$ , so the square root of $2 \frac{7}{9}$ is $\frac{5}{3}$ . By adding $\frac{3}{2}$ and $\frac{5}{3}$ , we get $\frac{19}{6}$ . Adding 19 and 6 yields us 25, so our answer is $\boxed{25}$

$\sqrt{2\frac{1}{4}}$ = $\sqrt{\frac{9}{4}}$ and $\sqrt{2\frac{7}{9}}$ = $\sqrt{\frac{25}{9}}$

Take root...

$\sqrt{\frac{9}{4}}$ = $\frac{3}{2} and \sqrt{\frac{25}{9}}$ = $\frac{5}{3}$

So, we have:

$\frac{3}{2} + \frac{5}{3}$

Calculate Least Common Multiple

$\frac{3}{2} + \frac{5}{3} = \frac{9+10}{6}$

$\frac{9+10}{6} = \frac{19}{6} = \frac{a}{b}$

Then... $a = 19$ and $b = 6$

$a+b = 19 + 9 => a + b = 25$

$\sqrt {2 \frac{1}{4} } + \sqrt {2 \frac{7}{9} }$

$\implies \sqrt \frac {9}{4} + \sqrt \frac {25}{9}$

$\implies \frac{3}{2} + \frac{5}{3}$

$\implies \frac{9 + 10}{6}$

$\implies \frac{19}{6} = \frac{a}{b}$

So, $a = 19$ and $b=6$

And $a+b = 19+6 = 25$

$\sqrt{2\frac{1}{4} } + \sqrt{2\frac{7}{9} } =\sqrt{\frac{9}{4} } + \sqrt{\frac{25}{9} }=\frac{3}{2} + \frac{5}{3}=\frac{9+10}{3*2}=\frac{19}{6}=>a=19, b=6=>a+b=25$

Express as an improper fraction . We have , sqrt.of 9/4+sqrt. of 25/9

= 3/2+5/3 = 19/6.

a+b = 25

$\sqrt{2\frac{1}{4}}+\sqrt{2\frac{7}{9}}$ $\sqrt{\frac{9}{4}}+\sqrt{\frac{25}{9}}$ $\frac{\sqrt{9}}{\sqrt{4}}+\frac{\sqrt{25}}{\sqrt{9}}$ $\frac{3}{2}+\frac{5}{3}$ $\frac{3\times3}{2\times3}+\frac{5\times2}{3\times2}$ $\frac{9}{6}+\frac{10}{6}$ $\frac{9+10}{6}$ $\frac{19}{6}$ So $a=19\;and\;b=6$ so $a+b=19+6=\boxed{25}$

Square root always means positive square root, because we dont multiply with -1 inside the radical sign. So sqrt{9/4} + sqrt{25/9} = 3/2+5/3 = 19/6. So answer is 25

sqrt(2 1/4) + sqrt(2 7/9) sqrt(9/4) + sqrt(25/9) 3/2 + 5/3 25 so ans is 25

convert the mixed fraction into a improper fraction(for both cases)and then find the square root of it (for both) and then add it to get the answer

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