Question

write whether 2 root 45+3 root 20/2 root 5 on simplifiacationgives a rational or irrational number

Answer 1

Hi ,

(2√45 + 3√20)/2√5

= (2√3×3×5 + 3√2×2×5 )/2√5

= ( 6√5 + 6√5 )/2√5

= 12√5/2√5

= 6

= Rational number

I hope this helps you.

: )

Answer 2

$\sf QUESTION: Write \ whether \ \ \dfrac{2\sqrt{45} + 3\sqrt{20}}{2\sqrt{5}} \ \ on \ simplication \ gives \ a \ rational \ or \ irrational\\number.$

$\huge \text{\sf \underline{Solution}}$

$\implies \ \sf \dfrac{2\sqrt{45} + 3\sqrt{20}}{2\sqrt{5}}$

$\implies \sf \ \dfrac{2\sqrt{3 \times 3 \times 5} \ + \ 3\sqrt{2 \times 2 \times 5}}{2\sqrt{5}}$

$\implies \sf \ \dfrac{2 \times 3\sqrt{5} \ + \ 3 \times 2\sqrt{5}}{2\sqrt{5}}$

$\implies \sf \ \dfrac{6\sqrt{5} \ + \ 6\sqrt{5}}{2\sqrt{5}}$

$\implies \sf \ \dfrac{12\sqrt{5}}{2\sqrt{5}}$

$\implies \sf \ \dfrac{12}{2}$

$\implies \sf \ 6$

6 is a Rational Number,

$\sf \implies \dfrac{2\sqrt{45} + 3\sqrt{20}}{2\sqrt{5}} \ \ on \ simplication \ gives \ a \ rational \ number.$