Question

simplest rationalisation factor of 3√40 is​
(a) 3 √25
(b) 3√5
(c) √40
(d) √5
with full solution​

Answer 1

Answer:

√10

Step-by-step explanation:

3√40= 3√2×2×2×5

=3×2√2×5

=6√10

=The procedure of multiplying a surd by another surd to get a rational number is called Rationalisation .The operands are called Rationalizing Factor (RF) of the other.Here √10

is the Rationalisation Factor

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Simplest rationalisation factor of 3√40 is

(a) 3 √25

(b) 3√5

(c) √40

(d) √5

EVALUATION

Here the given number is 3√40

CHECKING FOR OPTION : (a)

$\displaystyle \sf{ 3 \sqrt{40} \times 3 \sqrt{25} }$

$\displaystyle \sf{ = 9\sqrt{40 \times 25} }$

$\displaystyle \sf{ = 9\sqrt{1000} }$

$\displaystyle \sf{ = 9\sqrt{100 \times 10} }$

$\displaystyle \sf{ = 90\sqrt{ 10} }$

Which is an irrational number

So this option is not correct

CHECKING FOR OPTION : (b)

$\displaystyle \sf{ 3 \sqrt{40} \times 3 \sqrt{5} }$

$\displaystyle \sf{ = 9 \sqrt{40 \times 5} }$

$\displaystyle \sf{ = 9 \sqrt{200} }$

$\displaystyle \sf{ = 9 \sqrt{2 \times 100} }$

$\displaystyle \sf{ = 90 \sqrt{2 } }$

Which is an irrational number

So this option is not correct

CHECKING FOR OPTION : (c)

$\displaystyle \sf{ 3 \sqrt{40} \times \sqrt{40} }$

$\displaystyle \sf{ = 3 \sqrt{40 \times 40} }$

$\displaystyle \sf{ = 3 \times 40}$

$\displaystyle \sf{ = 120}$

Which is a rational number

So this option is correct

CHECKING FOR OPTION : (d)

$\displaystyle \sf{ 3 \sqrt{40} \times \sqrt{5} }$

$\displaystyle \sf{ = 3 \sqrt{40 \times 5} }$

$\displaystyle \sf = 3 \sqrt{200}$

$\displaystyle \sf = 3 \sqrt{2 \times 100}$

$\displaystyle \sf = 30 \sqrt{2}$

Which is an irrational number

So this option is not correct

FINAL ANSWER

Hence the correct option is (c) √40

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