Surds and Indices Questions and Answers

August 1, 2024

Surds and Indices Questions

Go through the entire page to know the Surds and Indices Questions and Answers using basic laws, rulaes and easy formulas.

Surds and Indices Questions and Answers

Basic Laws of Surds and Indices

Surds :

  • b√p = p(1/b)
  • b√pq = b√p * b√q
  • √(p/q) = (b√p )/(b√q )
  • (b√p)^{b} = p
  • a √b√p = ab√p
  • (b√p)^{a} = b√p^{a}

Indices :

  • (p^{a})^{b} = p^{ab}
  • p^{a}/p^{b} = p^{a-b}
  • (p/q)^{b} = p^{b}/q^{b}
  • p^{-1} = 1/p

Rule for solving Surds and Indices Questions and Answers

  • A number that is raised to the power zero will always be equals to one. For instance a0 = 1.
  • Surd b√p can be solved further only if the factor of p is a perfect square.
  • If surds are included in the denominator of a fraction, then it is required to rationalize the denominator through multiplying both denominator and numerator by an associated surd.
  • It is necessary to rationalize the denominator and to eliminate the surd in order to simplify different expressions.
  • In indices, the multiplication rule for solving the question with same base, the formula used is x^{a} * x^{b} = x^{a+b}
  • For division with same base formula used: x^{a} / x^{b} = (x)^{a-b}
  • Multiplication rule for same indices: x^{a} * y^{a} = (x*y)^{a}
  • Division rule for same indices: x^{a} / y^{a} = (x/y)^{a}
  • The square root or cube root of a positive real number is known as a surd only if its value is not exactly determined.
  • Two simple quadratic surd’s sum and difference are known as complementary surds to one another.
  • If m and n are both rational numbers and √p and √q are both surds and m + √p = n + √q then m = n and p = q
  • If m – √p = n – √q then m = n and p = q.
  • If m + √p = 0, then m = 0 and p = 0.
  • If m – √p = 0, then m = 0 and p = 0.

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Formulas to solve Surds and Indices
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1. Solve: (10)20 / (10)10

(10)^{10}

(10)^{10}

87.55%

(13)^{13}

(13)^{13}

2.6%

(5)^{2}

(5)^{2}

3.37%

(10)^{2}

(10)^{2}

6.48%

= (10)20 / (10)10
= (10)20-10
= (10)10

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2. If a and b are two whole numbers, such that ab = 25, then what will be the value of (a-1)b+1?

40

40

10.23%

50

50

16.65%

64

64

58.5%

10

10

14.62%

We know that 52 = 25

When we substitute, a=5, and b= 2, we get

= (5-1)2+1

= 4^{3}

= 64

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3. Find the value of (625)3/4.

500

500

3.12%

125

125

87.78%

225

225

6.3%

550

550

2.8%

= (54) ¾

= 53

= 125

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4. What will be the value of (√27)1/3?

3

3

32.68%

√3

√3

57.7%

9

9

8.41%

6

6

1.21%

= (√27)1/3

= (271/2)1/3

= 271/6

= (33) 1/6

= 3 ½

= √3

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5. Find the value of (150)6 x (150)x = (150)10.

16

16

3.38%

8

8

2.67%

4

4

91.44%

None of the above

None of the above

2.51%

= (150)6 x (150)x = (150)10

= 6 + x = 10

= x= 4

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6. Calculate the value of 'x' when 3(x-y) = 27 and 3(x+y) = 81.

3.5

3.5

76.66%

3

3

12.43%

5.5

5.5

4.75%

6

6

6.16%

3(x-y) = 27= 33

(x-y) =3------------------------------(1)

3(x+y) = 81 = 34

(x+y) = 4---------------------------(2)

When we add equation 1 and 2, we get

2x = 3 +4

2x= 7

X= 3.5

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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7. Solve 100236 / 100200 =?

100^{436}

100^{436}

8.45%

100^{36}

100^{36}

85.56%

100

100

2.87%

None of the above

None of the above

3.12%

100236 / 100200

=100 236-200

=10036

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8. If p and q are two whole numbers, and pq = 169, calculate the value of (p-3)(q+1).

10

10

5.07%

100

100

8.73%

1000

1000

82.06%

None of the above

None of the above

4.14%

pq = 169

132 = 169

Hence,

(p-3)(q+1) = (13-3)(2+1) = 103 =1000

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9. What will be the value of

25 x 25 x 25 x 25 = 5?

8

8

90.26%

18

18

1.75%

20

20

6.27%

22

22

1.72%

25 x 25 x 25 x 25

= 52 x 52 x 52 x 52

= 5(2+2+2+2)

= 58

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10. What will be the value of 5-14 – 5-15?

4 x 5^{15}

4 x 5^{15}

15.34%

4 x5^{-15}

4 x5^{-15}

66.5%

4500

4500

7.94%

None of the above

None of the above

10.22%

5-14 – 5-15

= 1/514 - 1/515

= 5/515 - 1/515

= (5-1)/515

= 4/515

= 4 x 5-15

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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Formulas to solve Surds and Indices
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