Question

What is the following product? (5sqrt4 - 4sqrt3)(5sqrt2 -4sqrt3)

Answer 1

Answer:

$\boxed{\approx 0,438}$

Step-by-step explanation:

We have the following product:

$(5\sqrt{4} - 4\sqrt{3})(5\sqrt{2} -4\sqrt{3})$

Applying distributive we have the following:

$(5\sqrt{4} - 4\sqrt{3})(5\sqrt{2} -4\sqrt{3}) \\ \\ 5 \times \sqrt{4}\sqrt{2}-5\times 4\sqrt{4}\sqrt{3}-4\times 5\sqrt{3}\sqrt{2}+4\times 4\sqrt{3}\sqrt{3}$

By solving the product of square root we have:

$5 \times5 \sqrt{4}\sqrt{2}-5\times 4\sqrt{4}\sqrt{3}-4\times 5\sqrt{3}\sqrt{2}+4\times 4\sqrt{3}\sqrt{3} \\ \\ 25\sqrt{(4)(2)}-20\sqrt{(4)(3)}-20\sqrt{(3)(2)}+16\sqrt{(3)(3)} \\ \\ 25\sqrt{8}-20\sqrt{12}-20\sqrt{6}+16\sqrt{9}$

But $\sqrt{9}=3$ then:

$25\sqrt{8}-20\sqrt{12}-20\sqrt{6}+16(3) \\ \\ 25\sqrt{8}-20\sqrt{12}-20\sqrt{6}+48 \approx \boxed{0,438}$