Question

(4 root 5 - 3 root 2) (3 root 5 + 5 root 2). Answer it plz fast 26 thanks I sure

Answer 1

Answer:

$\left(4\sqrt{5}-3\sqrt{2}\right)\left(3\sqrt{5}+5\sqrt{2}\right)=30+11\sqrt{10}\quad \left(\mathrm{Decimal:\quad }\:64.78505\dots \right)$

Step-by-step explanation:

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

$\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

$a=4\sqrt{5},\:b=-3\sqrt{2},\:c=3\sqrt{5},\:d=5\sqrt{2}$

$=4\sqrt{5}\cdot \:3\sqrt{5}+4\sqrt{5}\cdot \:5\sqrt{2}+\left(-3\sqrt{2}\right)\cdot \:3\sqrt{5}+\left(-3\sqrt{2}\right)\cdot \:5\sqrt{2}$

$\mathrm{Apply\:minus-plus\:rules}$

$+\left(-a\right)=-a$

$=4\cdot \:3\sqrt{5}\sqrt{5}+4\cdot \:5\sqrt{5}\sqrt{2}-3\cdot \:3\sqrt{2}\sqrt{5}-3\cdot \:5\sqrt{2}\sqrt{2}$

$\mathrm{Simplify}\:4\cdot \:3\sqrt{5}\sqrt{5}+4\cdot \:5\sqrt{5}\sqrt{2}-3\cdot \:3\sqrt{2}\sqrt{5}-3\cdot \:5\sqrt{2}\sqrt{2}$

$4\cdot \:3\sqrt{5}\sqrt{5}+4\cdot \:5\sqrt{5}\sqrt{2}-3\cdot \:3\sqrt{2}\sqrt{5}-3\cdot \:5\sqrt{2}\sqrt{2}$

$4\cdot \:3\sqrt{5}\sqrt{5}$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:3=12$

$=12\sqrt{5}\sqrt{5}$

$\sqrt{5}\sqrt{5}=5$

$=12\cdot \:5$

$\mathrm{Multiply\:the\:numbers:}\:12\cdot \:5=60$

$=60$

$4\cdot \:5\sqrt{5}\sqrt{2}$

$4\cdot \:5\sqrt{5}\sqrt{2}$

$\mathrm{Multiply\:the\:numbers:}\:4\cdot \:5=20$

$=20\sqrt{5}\sqrt{2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{ab}$

$\sqrt{5}\sqrt{2}=\sqrt{5\cdot \:2}$

$=20\sqrt{5\cdot \:2}$

$\mathrm{Multiply\:the\:numbers:}\:5\cdot \:2=10$

$=20\sqrt{10}$

$3\cdot \:3\sqrt{2}\sqrt{5}$

$3\cdot \:3\sqrt{2}\sqrt{5}$

$\mathrm{Multiply\:the\:numbers:}\:3\cdot \:3=9$

$=9\sqrt{2}\sqrt{5}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{ab}$

$\sqrt{2}\sqrt{5}=\sqrt{2\cdot \:5}$

$=9\sqrt{2\cdot \:5}$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:5=10$

$=9\sqrt{10}$

$3\cdot \:5\sqrt{2}\sqrt{2}$

$3\cdot \:5\sqrt{2}\sqrt{2}$

$\mathrm{Multiply\:the\:numbers:}\:3\cdot \:5=15$

$=15\sqrt{2}\sqrt{2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a$

$\sqrt{2}\sqrt{2}=2$

$=15\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:15\cdot \:2=30$

$=30$

$=60+20\sqrt{10}-9\sqrt{10}-30$

$\mathrm{Add\:similar\:elements:}\:20\sqrt{10}-9\sqrt{10}=11\sqrt{10}$

$=60+11\sqrt{10}-30$

$\mathrm{Subtract\:the\:numbers:}\:60-30=30$

$=30+11\sqrt{10}$