# Surds and Indices

## Surds and Indices

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 Question 1
(17)^3.5 x (17)^? = 17^8
 A 2.29 B 2.75 C 4.25 D 4.5
Question 1 Explanation:
Let (17)^3.5 x (17)^x = 17^8. Then, (17)^3.5 + x = 17^8. 3.5 + x = 8 ==> x = (8 - 3.5) ==> x = 4.5
 Question 2
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
 A 1.45 B 1.88 C 2.9 D 3.7
Question 2 Explanation:
x^z = y^2 10^(0.48z) = 10^(2 x 0.70) = 10^(1.40) 0.48z = 1.40 z =140/48 =35/12 =2.9 (approx.)
 Question 3
If 5^a = 3125, then the value of 5^(a - 3) is:
 A 25 B 125 C 625 D 1625
Question 3 Explanation:
5^a = 3125 5^a = 5^5 a = 5. 5^(a - 3) = 5^(5 - 3) = 5^2 = 2^5.
 Question 4
If 3^(x - y) = 27 and 3^(x + y) = 243, then x is equal to:
 A 0 B 2 C 4 D 6
Question 4 Explanation:
3^(x - y) = 27 = 3^3 x - y = 3 ....(i) 3^(x + y) = 243 = 3^5 x + y = 5 ....(ii) On solving (i) and (ii), we get x = 4.
 Question 5
(256)0.16 x (256)0.09 = ?
 A 4 B 16 C 64 D 256.25
Question 5 Explanation:
(256)^0.16 x (256)^0.09 = (256)^(0.16 + 0.09) ==> (256)^0.25b==> (256)^(25/100) ==> 4^(4*(1/4))1/4)=4
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