Question

what is the value of​

Answer 1

We are asked to find the exact value of the following equation:

$\longrightarrow \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{128 + \sqrt{256}}}}}$

Hint: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

• Radicand - The number under the inclusion bar of the radical sign.

• Product - The result of two numbers being multiplied together.

• Factors - One of two or more expressions thar are multiplier together to get a product.

Solution:

Simplifying each expressions by arranging the expressions in the radical sign and by performing addition.

$\implies \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{128 + \sqrt{256}}}}}$

$\implies \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{128 + 16}}}}$

$\implies \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{144}}}}$

$\implies \sqrt{41 + \sqrt{54 + \sqrt{88 + 12}}}$

$\implies \sqrt{41 + \sqrt{54 + \sqrt{100}}}$

$\implies \sqrt{41 + \sqrt{54 + 10}}$

$\implies \sqrt{41 + 8}$

$\implies \sqrt{49}$

$\implies \boxed{\:\:7\:\:}$

Hence, the value of given expression is 7.

Answer 2

$\rm⇢ \: \: \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{128 + \sqrt{256} } } } }$

$\rm⇢ \: \: \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{128 + 16} } } }$

$\rm⇢ \: \: \sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{144} } } }$

$\rm⇢ \: \: \sqrt{41 + 54 + \sqrt{88 + 12} }$

$\rm⇢ \: \: \sqrt{41 + \sqrt{54 + \sqrt{100} } }$

$\rm⇢ \: \: \sqrt{41 + \sqrt{54 + 10} }$

$\rm⇢ \: \: \sqrt{41 + \sqrt{64} }$

$\rm⇢ \: \: \sqrt{41 + 8}$

$\rm⇢ \: \: \sqrt{49}$

$\rm⇢ \: \: 7$

FINAL ANSWER :

The Value of $\sqrt{41 + \sqrt{54 + \sqrt{88 + \sqrt{128 + \sqrt{256} } } } } \:$ is 7 .