Exponents and radicals
Introduction :
The term exponents are the power value of one base number, which is integer or fraction or variables. This exponent number is placed on the right side and above of base number. Radical form is the ‘n’th root form. Which are square root values? Let us consider the number 82 or Xy
Here 8 are the base(x), 2 is the power of 2(y). We calculate `8^2= 8 xx 8 =64`
Definitions for exponents and radicals:
The term exponents are the power values, which are denoted to how many times to multiply with the power number.
The term radical is square root number. Example `sqrt (4), sqrt (3)` …
How to solve radical exponents:
If the given number is the radical number and it has power value means, multiply with the ‘n’ number of times. (n=given power value)
And the important note is `sqrt(y) xx sqrt(y) = y`
For example:
How to solve the given radical exponent value `sqrt (5) ^ (2)`
Solution:
Given:` sqrt (5) ^ (2)`
= `sqrt (5) * sqrt (5)`
=` 5.`
So, answer is 5.
Here let us going to do some more example problems and give some practice problems.
Example problems for how to solve radical exponents:
Example 1: How to solve the radical exponent values of given numbers.
(a) Solve: `sqrt (7) ^ (2)`
(b) Solve: `sqrt(5) ^ (4)`
Solutions:
(a) Given: `sqrt (7) ^ (2)`
= `sqrt (7) * sqrt (7)`
= 7
Answer is 7.
(b) Given: `sqrt (6) ^ (4)`
=` sqrt (6) * sqrt (6) * sqrt (6) * sqrt (6)`
=` 6 xx 6`
= 36.
Answer is 36.
Example 2: Solve given exponent radical number `sqrt (3) ^ (5).`
Solution:
Given: `sqrt (3) ^ (5)`
= `sqrt (3) * sqrt (3) * sqrt (3) * sqrt (3) * sqrt (3)`
= `(3 * 3) * sqrt (3)`
=` 9 * sqrt (3)`
Answer is `9 sqrt (3).`
Example 3: How to solve the exponent of radical `sqrt (9) ^ (4) + sqrt (4) ^ (2)`
Solution:
Given: `sqrt (9) ^ (4) + sqrt (4) ^ (2)`
=` [sqrt (9) xx sqrt (9) xx sqrt (9) xx sqrt (9)] + [sqrt (4) xx sqrt (4)]`
=` [(9 xx 9)] + [4]`
=` (81) + (4)`
= `85.`
Answer is 85.
Practice problems for solve exponent radicals:
Problem 1: How to solve given exponent radical number` sqrt (4) ^ (5)`
Answer is `16 sqrt (5).`
Problem 2: How to solve given exponent radical number `sqrt (12) ^ (3)`
Answer is `12 sqrt (12)`
Problem 3: How to solve given exponent radical number `sqrt (3) ^ (4) + sqrt (2) ^ 4`
Answer is 13.
The term exponents are the power value of one base number, which is integer or fraction or variables. This exponent number is placed on the right side and above of base number. Radical form is the ‘n’th root form. Which are square root values? Let us consider the number 82 or Xy
Here 8 are the base(x), 2 is the power of 2(y). We calculate `8^2= 8 xx 8 =64`
Definitions for exponents and radicals:
The term exponents are the power values, which are denoted to how many times to multiply with the power number.
The term radical is square root number. Example `sqrt (4), sqrt (3)` …
How to solve radical exponents:
If the given number is the radical number and it has power value means, multiply with the ‘n’ number of times. (n=given power value)
And the important note is `sqrt(y) xx sqrt(y) = y`
For example:
How to solve the given radical exponent value `sqrt (5) ^ (2)`
Solution:
Given:` sqrt (5) ^ (2)`
= `sqrt (5) * sqrt (5)`
=` 5.`
So, answer is 5.
Here let us going to do some more example problems and give some practice problems.
Example problems for how to solve radical exponents:
Example 1: How to solve the radical exponent values of given numbers.
(a) Solve: `sqrt (7) ^ (2)`
(b) Solve: `sqrt(5) ^ (4)`
Solutions:
(a) Given: `sqrt (7) ^ (2)`
= `sqrt (7) * sqrt (7)`
= 7
Answer is 7.
(b) Given: `sqrt (6) ^ (4)`
=` sqrt (6) * sqrt (6) * sqrt (6) * sqrt (6)`
=` 6 xx 6`
= 36.
Answer is 36.
Example 2: Solve given exponent radical number `sqrt (3) ^ (5).`
Solution:
Given: `sqrt (3) ^ (5)`
= `sqrt (3) * sqrt (3) * sqrt (3) * sqrt (3) * sqrt (3)`
= `(3 * 3) * sqrt (3)`
=` 9 * sqrt (3)`
Answer is `9 sqrt (3).`
Example 3: How to solve the exponent of radical `sqrt (9) ^ (4) + sqrt (4) ^ (2)`
Solution:
Given: `sqrt (9) ^ (4) + sqrt (4) ^ (2)`
=` [sqrt (9) xx sqrt (9) xx sqrt (9) xx sqrt (9)] + [sqrt (4) xx sqrt (4)]`
=` [(9 xx 9)] + [4]`
=` (81) + (4)`
= `85.`
Answer is 85.
Practice problems for solve exponent radicals:
Problem 1: How to solve given exponent radical number` sqrt (4) ^ (5)`
Answer is `16 sqrt (5).`
Problem 2: How to solve given exponent radical number `sqrt (12) ^ (3)`
Answer is `12 sqrt (12)`
Problem 3: How to solve given exponent radical number `sqrt (3) ^ (4) + sqrt (2) ^ 4`
Answer is 13.