Question

find the value of this ​

Answer 1

Question :

Find the value of $\tt\sqrt{15625}$. Using this evaluate : $\tt\sqrt{156.25}$ + $\tt\sqrt{1.5625}$.

To Find :

• The value of $\bf\sqrt{15625}$ and along with this, we need to evaluate $\bf\sqrt{156.25}$ + $\bf\sqrt{1.5625}$

Solution :

Taking out the value of $\tt\sqrt{15625}$ by using prime factorisation method.

$\begin{array}{c | c} \sf{ \blue{ \bf \underline{5}}}& \sf\underline{15625} \\ \blue{\bf{ \underline{5}}} & \sf \underline{3125} \\ \green{\pmb{\tt{ \underline{5}}}}& \sf \underline{645} \\ \green{\pmb{\tt{ \underline{5}}}} & \sf \underline{125} \sf \\ \pink{\bf{ \underline{5}}}& \sf \underline{25}& \\ \pink{\bf{ \underline{5}}}& \sf{ \underline{5}} \\ & \sf1\end{array}$

We got the prime factors as,

$\implies \tt \: 15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \\ \implies \tt \: 15625 = {5}^{2} \times {5}^{2} \times {5}^{2}$

We got the pairs of 5 so among them we'll take one 5 from each pair and will multiply to get the value..!

$\implies \tt \: 5 \times 5 \times 5 \\ \implies \tt \: \tt\sqrt{15625} = \bf \: 125$

∴ The value of $\tt\sqrt{15625}$ is 125.

Second part:

Now, doing the evaluation of $\bf\sqrt{156.25}$ + $\bf\sqrt{1.5625}$

$\implies \tt \sqrt{156.25} + \sqrt{1.5625} \\ \\ \implies \tt \sqrt \dfrac{15625}{100} + \sqrt \dfrac{15625}{10000} \\ \\ \tt \implies \dfrac{125}{10} + \dfrac{125}{100} \\ \\ \implies \tt 12.5 +1.25 \\ \\ \implies \large\underline{ \boxed{\pmb{ \tt{13.75}}}}$

∴ The evaluation of $\tt\sqrt{156.25}$ + $\tt\sqrt{1.5625}$ is 13.75.