Solve 3sqrt{98}div1/3sqrt{8}

$$3 \sqrt { 98 } \div \frac { 1 } { 3 } \sqrt { 8 }$$

Evaluate

$$252$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{3\times 7\sqrt{2}}{\frac{1}{3}}\sqrt{8}$$

Multiply 3 and 7 to get 21.

$$\frac{21\sqrt{2}}{\frac{1}{3}}\sqrt{8}$$

Divide 21\sqrt{2} by \frac{1}{3} by multiplying 21\sqrt{2} by the reciprocal of \frac{1}{3}.

$$21\sqrt{2}\times 3\sqrt{8}$$

Multiply 21 and 3 to get 63.

$$63\sqrt{2}\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$63\sqrt{2}\times 2\sqrt{2}$$

Multiply 63 and 2 to get 126.

$$126\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$126\times 2$$

Multiply 126 and 2 to get 252.

$$252$$

Factor

$$2^{2}\times 3^{2}\times 7$$