Question

(8root2+3root5) (3root2-6root3)

Answer 1

GIVEN :

The expression is $(8\sqrt{2}+3\sqrt{5})(3\sqrt{2}-6\sqrt{3})$

TO SIMPLIFY :

The given expression $(8\sqrt{2}+3\sqrt{5})(3\sqrt{2}-6\sqrt{3})$

SOLUTION :

Given expression is $(8\sqrt{2}+3\sqrt{5})(3\sqrt{2}-6\sqrt{3})$

Now solving the given expression as below :

$(8\sqrt{2}+3\sqrt{5})(3\sqrt{2}-6\sqrt{3})$

By using the Distributive property :

(x+y)(a+b) = (x+y)a+(x+y)b

$=8\sqrt{2}(3\sqrt{2}-6\sqrt{3})+3\sqrt{5}(3\sqrt{2}-6\sqrt{3})$

By using the Distributive property :

(x+y)a= xa+ya

$=8\sqrt{2}(3\sqrt{2})+8\sqrt{2}(-6\sqrt{3)+3\sqrt{5}(3\sqrt{2})+3\sqrt{5}(-6\sqrt{3})$

By using the square roots of 2 properties :

i) $\sqrt{x.x}=x$

ii) $\sqrt{x}.\sqrt{y}=\sqrt{xy}$

$=24(2)-48\sqrt{6}+9\sqrt{10}-18\sqrt{15}$

$=48-48\sqrt{6}+9\sqrt{10}-18\sqrt{15}$

∴  $(8\sqrt{2}+3\sqrt{5})(3\sqrt{2}-6\sqrt{3})=48-48\sqrt{6}+9\sqrt{10}-18\sqrt{15}$

∴ the given expression simplified form  into $48-48\sqrt{6}+9\sqrt{10}-18\sqrt{15}$