Solve 4sqrt{7}*1/8div1/16sqrt{28}

$$4 \sqrt { 7 } \times \frac { 1 } { 8 } \div \frac { 1 } { 16 } \sqrt { 28 }$$

Evaluate

$$112$$

Solution Steps

Multiply 4 and \frac{1}{8} to get \frac{4}{8}.

$$\frac{\frac{4}{8}\sqrt{7}}{\frac{1}{16}}\sqrt{28}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{1}{2}\sqrt{7}}{\frac{1}{16}}\sqrt{28}$$

Divide \frac{1}{2}\sqrt{7} by \frac{1}{16} by multiplying \frac{1}{2}\sqrt{7} by the reciprocal of \frac{1}{16}.

$$\frac{1}{2}\sqrt{7}\times 16\sqrt{28}$$

Multiply \frac{1}{2} and 16 to get \frac{16}{2}.

$$\frac{16}{2}\sqrt{7}\sqrt{28}$$

Divide 16 by 2 to get 8.

$$8\sqrt{7}\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$8\sqrt{7}\times 2\sqrt{7}$$

Multiply 8 and 2 to get 16.

$$16\sqrt{7}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$16\times 7$$

Multiply 16 and 7 to get 112.

$$112$$

Factor

$$2^{4}\times 7$$