Question

5. Find the value of the following:
a.
$\sqrt{ \frac{46}{169} }$
​

Answer 1

Answer:

→ 7/13

Step-by-step explanation:

Question :

Find the value of the following :

$\sf \longrightarrow \sqrt{ \dfrac{49}{169} }$

Solution :

$\sf \longrightarrow \sqrt{ \dfrac{49}{169} }$

$\bigstar\;\sf \pink{Finding \; factors\; of \;\bf 49 : }$

$\:\: \begin{array}{c|c} {\underline{\sf{7}}}&{\underline{\sf{\:\:49 \:\:}}}\\ {\underline{\sf{7}}}& \underline{\sf{\:\:7 \:\:}} \\\underline{\sf{}}&\underline{\sf{\:1\:}} \end{array}$

$\implies \sf\: 7 \times 7$

$\bigstar\;\sf \red{Finding \; factors\; of \;\bf 169 : }$

$\:\: \begin{array}{c|c} {\underline{\sf{13}}}&{\underline{\sf{\:\:169\:\:}}}\\ {\underline{\sf{13}}}& \underline{\sf{\:\:13 \:\:}} \\\underline{\sf{}}&\underline{\sf{\:1\:}} \end{array}$

$\implies \sf\: 13 \times 13$

Now, let's solve the question!

$\sf \longrightarrow \sqrt{ \dfrac{7 \times 7}{13 \times 13} }$

$\sf \longrightarrow \sqrt{ \dfrac{ \underline{7 \times 7}}{ \underline{13 \times 13}} }$

$\red{ \sf \longrightarrow \underline{\boxed{{ \bf \dfrac{7}{13 } }} } \: \bigstar}$

Hence, value of the expression is 7/13.