# Surds and Indices Questions and Answers

## 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.

## 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.

### Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

## Also Check Out

1. Solve: (10)20 / (10)10

$(10)^{10}$

$(10)^{10}$

89.8%

$(13)^{13}$

$(13)^{13}$

1.9%

$(5)^{2}$

$(5)^{2}$

2.77%

$(10)^{2}$

$(10)^{2}$

5.54%

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

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

10.32%

50

50

15.54%

64

64

58.5%

10

10

15.64%

We know that 52 = 25

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

= (5-1)2+1

= $4^{3}$

= 64

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

500

500

3.1%

125

125

88.13%

225

225

6.19%

550

550

2.58%

= (54) ¾

= 53

= 125

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

3

3

32.44%

√3

√3

57.59%

9

9

8.63%

6

6

1.34%

= (√27)1/3

= (271/2)1/3

= 271/6

= (33) 1/6

= 3 ½

= √3

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

16

16

3.44%

8

8

3.01%

4

4

90.98%

None of the above

None of the above

2.58%

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

= 6 + x = 10

= x= 4

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

3.5

3.5

76%

3

3

12.44%

5.5

5.5

6.32%

6

6

5.25%

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

7. Solve 100236 / 100200 =?

$100^{436}$

$100^{436}$

6.85%

$100^{36}$

$100^{36}$

88.99%

100

100

1.48%

None of the above

None of the above

2.68%

100236 / 100200

=100 236-200

=10036

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

10

10

5.62%

100

100

9.5%

1000

1000

80.18%

None of the above

None of the above

4.7%

pq = 169

132 = 169

Hence,

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

9. What will be the value of

25 x 25 x 25 x 25 = 5?

8

8

89.6%

18

18

1.64%

20

20

6.57%

22

22

2.19%

25 x 25 x 25 x 25

= 52 x 52 x 52 x 52

= 5(2+2+2+2)

= 58

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

4 x $5^{15}$

4 x $5^{15}$

13.37%

4 x$5^{-15}$

4 x$5^{-15}$

68.7%

4500

4500

6.96%

None of the above

None of the above

10.98%

5-14 – 5-15

= 1/514 - 1/515

= 5/515 - 1/515

= (5-1)/515

= 4/515

= 4 x 5-15

×

## Get over 200+ course One Subscription

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others