Question

Simplify the square root of 5 times the cube root of 5.

five to the five sixths power
five to the one sixth power
five to the two thirds power
five to the seven sixths power

Answer 1

Option B 5^ 2/3 is incorrect

Explanation:

i took the test and got it wrong Im not sure of the correct answer

Answer 2

Option 3 - five to the two thirds power

Explanation:

Given : Expression 'the square root of 5 times the cube root of 5'.

To find : Simplify the expression ?

Solution :

Writing expression in numeric form,

The cube root of 5 means
`\sqrt[3]{5}`

The square root of 5 times the cube root of 5 means
`\sqrt{5\sqrt[3]{5}}`

Now, simplify the expression

`\sqrt{5\sqrt[3]{5}}=\sqrt{5* (5)^{(1)/(3)}}`

`\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{1+(1)/(3)}}`

`\sqrt{5\sqrt[3]{5}}=\sqrt{(5)^{(4)/(3)}}`

`\sqrt{5\sqrt[3]{5}}=((5)^{(4)/(3)})^{(1)/(2)}`

`\sqrt{5\sqrt[3]{5}}=(5)^{(4)/(3)* (1)/(2)}`

`\sqrt{5\sqrt[3]{5}}=(5)^{(2)/(3)}`

The expression is five to the two thirds power.

Therefore, Option 3 is correct.