Question

If 3√( a+1 ), 4√5 are similar surds, then a = ?​

Answer 1

Final Answer:

When $3\sqrt{(a+1)},\;4\sqrt{5}$ are similar surds, then the value of a is $\frac{71}{9}$.

Given:

The surds $3\sqrt{(a+1)},\;4\sqrt{5}$ are similar.

To Find:

When $3\sqrt{(a+1)},\;4\sqrt{5}$ are similar surds, then the value of a is to be found.

Explanation:

The surd refers to the entity indicating the corresponding root with the accurate radical sign on the number referred.

The surds follow certain defined rules or laws for the mathematical operations of addition, subtraction, multiplication, etc.

Step 1 of 2

As per the statement in the given problem, write the following equation.

$3\sqrt{(a+1)}=4\sqrt{5}$

Step 2 of 2

In accordance with the laws of surds, solve the following equation.

$3\sqrt{(a+1)}=4\sqrt{5}\\\\(3\sqrt{a+1})^2=(4\sqrt{5})^2\\\\3^2(a+1)=4^2\times (\sqrt{5})^2\\\\9(a+1)=80\\\\a+1=\frac{80}{9}\\\\a=\frac{80}{9} -1\\\\a=\frac{80-9}{9} \\\\a=\frac{71}{9}$

Therefore, the required value of a is $\frac{71}{9}$, when $3\sqrt{(a+1)},\;4\sqrt{5}$ are similar surds.$\frac{71}{9}$

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