Question

If (√5+√2)÷√7=⅐(√35+a).
Let us calculate the value of a.​

Answer 1

Step-by-step explanation:

$\tt\red{\boxed{\boxed{\tt Given :\frac{(\sqrt{5}+\sqrt{2})}{\sqrt{7}}=\frac{1}{7}(\sqrt{35}+a)}}}$

1. Simplify $\frac{1}{7}(\sqrt{35}+a)$ to $\frac{\sqrt{35}+a}{7}$

.

$\tt\green{\frac{\sqrt{5}+\sqrt{2}}{\sqrt{7}}=\frac{\sqrt{35}+a}{7}}$

2 Multiply both sides by 7.

$\tt\blue{\implies\frac{\sqrt{5}+\sqrt{2}}{\sqrt{7}}\times 7=\sqrt{35}+a}$

3 Simplify $\tt\frac{\sqrt{5}+\sqrt{2}}{\sqrt{7}}\times 7$ to $\tt\frac{(\sqrt{5}+\sqrt{2})\times 7}{\sqrt{7}}$

.

$\tt\orange{\implies\frac{(\sqrt{5}+\sqrt{2})\times 7}{\sqrt{7}}=\sqrt{35}+a}$

4 Regroup terms.

$\tt\pink{\implies\frac{7(\sqrt{5}+\sqrt{2})}{\sqrt{7}}=\sqrt{35}+a}$

5 Subtract $\tt\sqrt{35}$ from both sides.

$\tt\red{\implies\frac{7(\sqrt{5}+\sqrt{2})}{\sqrt{7}}-\sqrt{35}=a}$

6 Switch sides.

$\tt\purple{\implies a=\frac{7(\sqrt{5}+\sqrt{2})}{\sqrt{7}}-\sqrt{35}}$

Decimal Form: 3.741657