What is the value of \sqrt{4^5 + 4^5 + 4^5 + 4^5}? — GRE General Test

What is the value of $\sqrt{4^5 + 4^5 + 4^5 + 4^5}$ ?

Combining the four terms inside the radical gives

4 \times 4^5 = 4^6

. Taking the square root yields

\sqrt{4^6} = 4^3

, which evaluates to 64.

Rewrite the sum inside the radical as multiplication

4^5 + 4^5 + 4^5 + 4^5 = 4 \times 4^5

Adding four identical terms is equivalent to multiplying the term by 4.

Apply the product rule for exponents

4^1 \times 4^5 = 4^{1+5} = 4^6

When multiplying exponential expressions with the same base, add their exponents.

Simplify the radical expression

\sqrt{4^6} = (4^6)^{1/2} = 4^3 = 64

Taking the square root of a power is equivalent to dividing the exponent by 2.

Exponent Addition and Radical Laws

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