Solve sqrt{7}(sqrt{42}-sqrt{48})

$$\sqrt { 7 } ( \sqrt { 42 } - \sqrt { 48 } )$$

Evaluate

$$7\sqrt{6}-4\sqrt{21}\approx -1.18387458$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\sqrt{7}\left(\sqrt{42}-4\sqrt{3}\right)$$

Use the distributive property to multiply \sqrt{7} by \sqrt{42}-4\sqrt{3}.

$$\sqrt{7}\sqrt{42}-4\sqrt{7}\sqrt{3}$$

Factor 42=7\times 6. Rewrite the square root of the product \sqrt{7\times 6} as the product of square roots \sqrt{7}\sqrt{6}.

$$\sqrt{7}\sqrt{7}\sqrt{6}-4\sqrt{7}\sqrt{3}$$

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

$$7\sqrt{6}-4\sqrt{7}\sqrt{3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$7\sqrt{6}-4\sqrt{21}$$