Question

Add :-

= 2√2 + 5√3 and √2 - 3√3

Multiply :-

= 6√5 by 2√5

Divide :-

= 8√15 by 2√3

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Answer 1

Answer:

Add

$2 \sqrt{2} + 5 \sqrt{3} + \sqrt{2} - 3 \sqrt{3} \\ = 2 \sqrt{2} + \sqrt{2} + 5 \sqrt{3} - 3 \sqrt{3} \\ = 3 \sqrt{2 } + 2 \sqrt{3}$

Multiply

$6 \sqrt{5} \times 2 \sqrt{5} \\ = 6 \times 2 \times \sqrt{5} \times \sqrt{5} \\ = 12 \times 5 \\ = 60$

Divide

$\frac{8 \sqrt{15} }{2 \sqrt{3} } \\ = \frac{8 \sqrt{3 \times 5} }{2 \sqrt{3} } \\ = \frac{8 \times \sqrt{3} \times \sqrt{5} }{2 \sqrt{3} } \\ = 4 \sqrt{5}$

Answer 2

Answer :-

a) We are given two irrational numbers, So first by writing the like terms together, we can add them :-

2√2 + 5√3 + √2 - 3√3

Like terms are :- ( 2√2 and √2 ) & ( 5√3 - 3√3 )

So,

( 2√2 + √2 ) + ( 5√3 - 3√3 )

= 3√2 + 2√3

( As these are unlike terms we can't add them )

Hence,

$\boxed{\sf 2\sqrt{2} + 5\sqrt{3} + \sqrt{2} - 3\sqrt{3} = 3\sqrt{2} + 2\sqrt{3}}$

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b) Here, we have to multiply two irrational number which are - 6√5 and 2√5

In multiplication of irrational numbers we multiply rational numbers separately and irrational separately -

So,

6√5 × 2√5 = ( 6 × 2 ) × (√5 × √5)

= 12 × 5

= 60

Hence,

$\boxed{\sf 6\sqrt{5} × 2\sqrt{5} = 60}$

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c) Here, we can split √15 into √5 and √3 and then we can simply solve :-

$\sf \frac{8\sqrt{15}}{2\sqrt{3}} = \frac{\cancel8 \times \sqrt{5} \times \cancel{\sqrt{3}}}{\cancel2\cancel{\sqrt{3}}}$

$\sf = 4\sqrt{15}$

$\boxed{\sf \frac{8\sqrt{15}}{2\sqrt{3}} = 4\sqrt{15}}$