Table of contents |
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What are Indices? |
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Solved Examples on Indices |
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Surds |
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Difference between Surds and Indices |
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Solved Examples on Surds & Indices |
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Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
Let's look at some solved examples for Indices
Q.1. Multiply x4y3z2 and xy5z-1
Ans:
x4y3z2 and xy5z-1
= x4.x .y3.y5.z2.z-1
= x4+1.y3+5.z2-1
= x5.y8.z
Q.2. Solve a3b2/a2b4
Ans:
a3b2/a2b4
= a3-2b2-4
= a1b-2
= a b-2
= a/b2
Q.3. Find the value of 272/3
Ans:
3√272
= 32
= 9
If then the value of x is:
The different types of surds are as follows:
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Introduction: Indices and Surds
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Example 1: 163/2 + 16-3/2 = ?
We know, by laws of exponents,
am x an = am+n
a-m = 1/am
163/2 + 1/163/2
(161/2)3 + 1/(161/2)3
(42 x 1/2)3 + 1/(42 x 1/2)3
43 + 1/43
64 + 1/64
(64 x 64+ 1)/64
= (4096+1)/64
= 4097/64
Example 2: If (1/5 )3a = 0.008 Find the value of ( 0.25)a
(1/5 )3a = 0.008 = 8/1000 = 1/125 = (1/5 )3
Apply the Algebra Law and Solve the equation.
⇒ 3a = 3
∴ a = 1
∴ ( 0.25 )a = ( 0.25 )1 = 0.25
Example 3: Write down the conjugate of 5√3 + √2
The conjugate of 5√3 + √2 is 5√3 - √2.
Example 4: Rationalise the denominator: 1/[(8√11 )- (7√5)]
Given: 1/[(8√11 )- (7√5)]
It is known that the conjugate of (8√11 )- (7√5) is (8√11 )+(7√5)
To rationalize the denominator of the given fraction, multiply the conjugate of denominator on both numerator and denominator.
= [1/[(8√11 )- (7√5)]]× [[(8√11 )+ (7√5)]/[(8√11 )+(7√5)]]
= [(8√11 )+ (7√5)]/[(8√11 )2-(7√5)2]
= [(8√11 )+ (7√5)]/[704- 245]
= [(8√11 )+ (7√5)]/459
Example 5: Multiply √7 x √2
√7 x √2 = √(7 x 2) = √14
Example 6: Divide √10 by √5.
√10/√5 = √(10/5) = √2
Example 7: Solve √x + 2√x.
√x + 2√x = 3√x
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1. What are indices? | ![]() |
2. Can you provide some examples of indices problems? | ![]() |
3. What are surds? | ![]() |
4. How are surds different from indices? | ![]() |
5. Can you provide some examples of surds and indices problems? | ![]() |