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Since,
 = 0.875 (Terminating decimal)
(Irrational)
93/300 = 31/100 = 0.31 (Terminating decimal)
190/30 = (Repeating decimal)
∵ Repeating and terminating decimals are rational numbers.
(243/32)^{0.8} then the value of ‘t’ will be
Here
⇒ (3)^{3(nm)} = (3)^{x}
⇒ x = 3(m – n) = 3 [m  n = 1]
If √3 = 1.732 and √5 = 2.236 then the value of is
We have
= 3(2.236+1.732)
= 3(3.968)
= 11.904
= 10 + 3 – 7√3 = α + b
= 13 – 7√3 = α + b√3
⇒ α = 13, b = –7
2^{m} x 2^{m} =2^{2}
⇒ (2)^{2m} = (2)^{2}
⇒ m = 1
Substituting the value of m in,
Here
Similarly
Rearranging all the terms in the required pattern, we have
= 3 + 2 = 5
∵ 10^{x} = 64 ⇒ (10x)^{1/2} = (64)^{1/2} = 8
∴ 10^{x/2} = 8 ⇒ = 8 x 10 = 80
∵ x^{–2} = 64
⇒ x^{1} = 8
⇒ x = 1/8
If x = 1– √2, then the value of(x  1/x)^{3} is
Given x = 2 + √3 then
Rationalising the denominator we have
∴ x = 5, y = 3
Given n = then x = 0.24545
10x = 2.4545 ...(i)
and 100x = 24.54545
and 1000x = 245.454545 ...(iii)
Subtracting eq (i) and eq (iii), we get
990x = 243
⇒ x = 243/990 = 27/110
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