Simplify the expression 37 31/2

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Simplify the expression inside the parentheses. 64 − 6 = 58 Step 2: Substitute the simplified value back into the expression. 37 √3^(1/2) Step 3: Convert the exponent 1/2 to a square root. (58)^(1/2) = √(58) Step 4: Rewrite the expression. 37 √[3]√(58) Step 5: Combine the roots. The cube root of a square root is equivalent to the sixth root. This can be written using fractional exponents as ( (58)^(1/2) )^(1/3) = 58^((1/2) × (1/3)) = 58^(1/6). 37 √[6]58 Step 6: Check if the number under the radical can be simplified. The prime factorization of 58 is 2 × 29. Since there are no factors raised to the power of 6, the radical cannot be simplified further. The simplified expression is: 37 √[6]58

Simplify the expression 37 31/2

Answer

Step-by-step solution

Simplify the expression inside the parentheses.

Substitute the simplified value back into the expression.

Convert the exponent $1/2$ to a square root.

Rewrite the expression.

Combine the roots.

Check if the number under the radical can be simplified.

Try one yourself

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Simplify the expression 37 31/2

Answer

Step-by-step solution

Simplify the expression inside the parentheses.

Substitute the simplified value back into the expression.

Convert the exponent 1/21/21/2 to a square root.

Rewrite the expression.

Combine the roots.

Check if the number under the radical can be simplified.

Try one yourself

Still stuck on this one?

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Convert the exponent $1/2$ to a square root.