Solve sqrt{27}*sqrt{1/3}=quad(1)

$$\sqrt { 27 } \times \sqrt { \frac { 1 } { 3 } } = \quad ( 1 )$$

Verify

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\sqrt{3}\sqrt{\frac{1}{3}}=1$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$3\sqrt{3}\times \frac{\sqrt{1}}{\sqrt{3}}=1$$

Calculate the square root of 1 and get 1.

$$3\sqrt{3}\times \frac{1}{\sqrt{3}}=1$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$3\sqrt{3}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=1$$

The square of \sqrt{3} is 3.

$$3\sqrt{3}\times \frac{\sqrt{3}}{3}=1$$

Cancel out 3 and 3.

$$\sqrt{3}\sqrt{3}=1$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3=1$$

Compare 3 and 1.

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