If a = 3 and b = 2, what is the value of the expression \sqrt{a^4 - b^5}? — ACT

If $a = 3$ and $b = 2$ , what is the value of the expression $\sqrt{a^4 - b^5}$ ?

Cevap: 7

The value of the expression is 7.

Evaluating the exponents yields

3^4 = 81

and

2^5 = 32

. Substituting these values under the radical gives

\sqrt{81 - 32} = \sqrt{49}

. Evaluating the square root of 49 gives the correct value of 7.

Evaluate the terms with exponents using the given values

a = 3

and

b = 2

a^4 = 3^4 = 81

and

b^5 = 2^5 = 32

Exponent operations must be evaluated before performing subtraction or taking the root.

Substitute the evaluated terms back into the radical expression and subtract.

\sqrt{81 - 32} = \sqrt{49}

Simplifying the expression under the radical is necessary before taking the square root.

Find the square root of the simplified value.

\sqrt{49} = 7

Evaluating the square root of 49 completes the simplification of the expression.

Evaluating expressions involving exponents, subtraction, and square roots

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