Solve isqrt{12}(isqrt{5}-sqrt{7})

$$i \sqrt { 12 } ( i \sqrt { 5 } - \sqrt { 7 } )$$

Evaluate

$$-2\sqrt{21}i-2\sqrt{15}\approx -7.745966692-9.16515139i$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$i\times 2\sqrt{3}\left(i\sqrt{5}-\sqrt{7}\right)$$

Use the distributive property to multiply 2i\sqrt{3} by i\sqrt{5}-\sqrt{7}.

$$-2\sqrt{3}\sqrt{5}-2i\sqrt{3}\sqrt{7}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$-2\sqrt{15}-2i\sqrt{3}\sqrt{7}$$

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

$$-2\sqrt{15}-2i\sqrt{21}$$

Real Part

$$-2\sqrt{15}$$