Check 2-45 - 3-20-2-5 is rational number and irrational number-

2√(45)+3√(20)2√(5) =2√((3.3).5)+3√((2.2).5)2√(5) =2.3√(5)+3.2√(5)2√(5) =6√(5)+6√(5)2√(5) =12√(5)2√(5) =6 Hence, it is a rational n ...

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Byju's Answer

Standard X

Mathematics

Number Theory: Interesting Results

Check 2√45 ...

Question

Check $\frac{2 \sqrt{45} + 3 \sqrt{20}}{2 \sqrt{5}}$ is rational number and irrational number?

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Solution

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

$= \frac{2 \sqrt{(3.3) .5} + 3 \sqrt{(2.2) .5}}{2 \sqrt{5}}$

$= \frac{2.3 \sqrt{5} + 3.2 \sqrt{5}}{2 \sqrt{5}}$

$= \frac{6 \sqrt{5} + 6 \sqrt{5}}{2 \sqrt{5}}$

$= \frac{12 \sqrt{5}}{2 \sqrt{5}}$

$= 6$

Hence, it is a rational number.

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Similar questions

Q. Prove that

(2 \sqrt{3} + \sqrt{5})

is an irrational number. Also check whether

(2 \sqrt{3} + \sqrt{5}) (2 \sqrt{3} - \sqrt{5})

is rational or irrational

Q. Write whether

\frac{2 \sqrt{45} + 3 \sqrt{20}}{2 \sqrt{5}}

on simplification gives a rational or an irrational number.

Q. Write whether

\frac{2 \sqrt{45} + 3 \sqrt{20}}{2 \sqrt{5}}

on simplification gives as rational or an irrational number

(a) Find ten rational number between - $\frac{2}{5}$ and $\frac{1}{2}$ .

(b) Insert 5 rational numbers and 2 irrational numbers between $\sqrt{2}$ and $\sqrt{3}$ .

[4 MARKS]

Check whether (√3+2)^2 is rational or irrational

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Check 2√45+3√202√5 is rational number and irrational number?

2√45+3√202√5=2√(3.3).5+3√(2.2).52√5=2.3√5+3.2√52√5=6√5+6√52√5=12√52√5=6Hence, it is a rational number.

Check $\frac{2 \sqrt{45} + 3 \sqrt{20}}{2 \sqrt{5}}$ is rational number and irrational number?

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

$= \frac{2 \sqrt{(3.3) .5} + 3 \sqrt{(2.2) .5}}{2 \sqrt{5}}$

$= \frac{2.3 \sqrt{5} + 3.2 \sqrt{5}}{2 \sqrt{5}}$

$= \frac{6 \sqrt{5} + 6 \sqrt{5}}{2 \sqrt{5}}$

$= \frac{12 \sqrt{5}}{2 \sqrt{5}}$

$= 6$

Hence, it is a rational number.