Question

Write whether 2√
$2 \sqrt{45} + 3 \sqrt{20} \div 2 \sqrt{5}$
on simplification gives a rational number or irrational number. [​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$\tt \red{ \implies2 \sqrt{45} + 3 \sqrt{20} \div 2 \sqrt{5}}$

$\tt \pink{ \implies2\times 3\sqrt{5}+3\times 2\sqrt{5}\div 2\sqrt{5}}$

$\tt \blue{ \implies6 \sqrt{5} +65 \sqrt{5} ÷25}$

Use this rule: $\tt a\div \frac{b}{c}=a\times \frac{c}{b}$

.

$\tt \orange{ \implies6\sqrt{5}+6\sqrt{5}\times \frac{1}{2}\sqrt{5}}$

Use this rule: $\tt\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$

$\tt \green{ \implies6\sqrt{5}+\dfrac{6\sqrt{5}\times 1\times \sqrt{5}}{2}}$

$\tt \purple{ \implies6 \sqrt{5} + \dfrac{6 \sqrt{25} }{2} }$

$\tt \red{ \implies6 \sqrt{5} + \dfrac{ \cancel{6} {}^{3} \times 5} {\cancel{2} } }$

$\tt \purple{ \implies6 \sqrt{5} + 15 }$