Question

√(9-√(3+√(5-√(3+√(169))))

simplify​

Answer 1

Answer:

$\sqrt{7 } = 2.645$

Answer 2

Given,

An expression: √(9-√(3+√(5-√(3+√(169))))

To find,

The simplified value of the expression.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

For any number a,

√(a^2) = a

{Statement-1}

On simplifying the given expression, we get;

√(9-√(3+√(5-√(3+√(169))))

= √(9-√(3+√(5-√(3+√(13^2))))

= √(9-√(3+√(5-√(3+13)))

{according to statement-1}

= √(9-√(3+√(5-√(16)))

= √(9-√(3+√(5-√(4^2)))

= √(9-√(3+√(5-4)))

{according to statement-1}

= √(9-√(3+√(1)))

= √(9-√(3+√(1^2)))

= √(9-√(3+1))

{according to statement-1}

= √(9-√4)

= √(9-√(2^2))

= √(9-2)

{according to statement-1}

= √7 = 2.645 (approx.)

Hence, the simplified value of the given expression is approximately equal to 2.645.