Question

write whether 2root45+3root20/2root5 on simplification gives a rational number or irrational number

Answer 1

Hello,
2√45+3√20/2√5;
=√5×[2√45+3√20/2√5];
=√5×(2√45+3√20/2)/2×(√5×√5);
=2√45·5+3√20·5/2×5;
=2√9·5·5+3√4·5·5/10;
=2√9·25+3√4·25/10;
=2×3×5+3×2×5/10;
=30+30/10;
=60/10;
=6

bye :)

Answer 2

Answer:

The required solution 6 is a rational number.

Step-by-step explanation:

Given: Expression ${\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}}$

To find : Solution of the expression and write whether on simplification gives a rational number or irrational number?

Solution :

$\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}} \\\\=\frac{2\sqrt{3\times3\times5}+3\sqrt{2\times2\times5}{2\sqrt{5}}}\\\\=\frac{2.3\sqrt{5}+3.2\sqrt{5}}{2\sqrt{5}}\\\\=\frac{12\sqrt{5}}{2\sqrt{5}}\\\\=6$

Therefore, The required solution 6 is a rational number.