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# Simplify square root of 2 multiplied by the cube root of 2.

Let's look into the product law a^{m} × a^{n} = a^{m+n} under the exponent rules.

## Answer: Square root of 2 multiplied by the cube root of 2 is equal to 2^{(5/6)}.

Let's put the question in form of an expression and solve it further.

**Explanation:**

As per the product law,

a^{m} × a^{n} = a^{m+n}

The square root of 2 = 2^{1⁄2}

Cube root of 2 = 2^{1⁄3}

Here we have a = 2, m =^{ }1/2^{ }and n =_{ }1/3,

⇒ 2^{1/2} × 2^{1/3}

⇒ 2^{(1/2 + 1/3)}

⇒ 2^{(3+2)/6}

⇒ 2^{5/6}

### Hence, the square root of 2 multiplied by the cube root of 2 is 2^{5/6}.

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