(i) Simplify the following :
(ii) Simplify the following :
(iii) Simplify the following :
(iv) Simplify the following :
(v) Simplify the following :
(vi) Simplify the following :
(vii) Simplify the following :
(viii) Simplify the following :
(ix) Simplify the following :
(i) Answer.
Solution.
We know that,
45 =
20 =
So we get
Hence the answer is
(ii) Answer.
Solution. We have,
We know that,
So we get
Taking LCM (3,4) = 12
(iii) Answer.
Solution. We have
We know that
12 =
6 =
So we get,
=
=
Hence the number is .
(iv)Answer.
Solution. We have,
We know that
28 =
So we can write,
=
=
Hence the answer is
(v) Answer.
We know that
27 =
So, =
(Rationalising the denominator)
(Taking common)
Now LCM (1,1,3) = 3
Hence the answer is 19.63
(vi) Answer.
Solution. Given,
We know that (a + b)2 = a2 – 2ab + b2
Comparing the given equation with the identity, we get:
= 3 + 2 –
Hence the answer is
(vii) Answer. 0
Solution. We have,
We know that
81 =
216 =
32 =
225 =
So,
= 3 – 8 × 6 + 15 × 2 + 15
= 3 – 48 + 30 + 15
= – 45 + 45
= 0
Hence the answer is 0
(viii) Answer.
Solution. We have,
We know that, 8 =
So,
Hence the answer is
(ix) Answer.
Solution. We have,
LCM (3,6) = 6
Hence the answer is .