PROPERTIES OF RADICALS WORKSHEET
Properties of radicals worksheet :
Worksheet on properties of radicals is much useful to the students who would like to practice problems on radicals.
Properties of radicals worksheet - Problems
1) Simplify the following √5 x √18
2) Simplify the following ∛7 x ∛8
3) Simplify the following 3√35 ÷ 2√7
4) Simplify the following radical expression
7 √30 + 2 √75 + 5 √50
5) Simplify the following radical expression
√27 + √105 + √108 + √45
6) Simplify the following radical expression
√45 + 3 √20 + √80 - 4 √40
7) Simplify the following radical expression
3√5 + 2√95 + 3√117 - √78
8) Simplify the following radical expression
3 √32 - 2√8 + √50
9) Simplify the following radical expression
2 √12 - 3√27 - √243
10) Simplify the following radical expression
√54 - √2500 - √24
11) Simplify the following radical expression
√45 - √25 - √80
12) Simplify the following radical expression
5√95 - 2√50 - 3√180
13) Solve for "x" :
2√x - 2 = 10
Properties of radicals worksheet - Solution
Problem 1:
Simplify the following √5 x √18
Solution :
= √5 x √18
According to the laws of radical,
= √(5 x 18) ==> √(5 x 3 x 3) ==> 3 √5
Problem 2 :
Simplify the following ∛7 x ∛8
Solution :
= ∛7 x ∛8
According to the laws of radical,
= ∛(7 x 8) ==> ∛(7 x 2 x 2 x 2) ==> 2 ∛7 x 2 ==> 2 ∛14
Problem 3 :
Simplify the following 3√35 ÷ 2√7
Solution :
= 3√35 ÷ 2√7
According to the laws of radical,
= (3/2) √(35/7) ==> (3/2)√5
Problem 4 :
Simplify the following radical expression
7 √30 + 2 √75 + 5 √50
Solution :
= 7 √30 + 2 √75 + 5 √50
First we have to split the given numbers inside the radical as much as possible.
= √(5 x 2 x 3) + √(5 x 5 x 3) + √(5 x 5 x 2)
Here we have to keep √30 as it is.
= √30 + 5 √3 + 5 √2
Problem 5 :
Simplify the following radical expression
√27 + √105 + √108 + √45
Solution :
= 3 √5 + 2√95 + 3√117 - √78
First we have to split the given numbers inside the radical as much as possible
= √(3 x 3 x 3) + √(5 x 3 x 7) +
√(3 x 3 x 3 x 2 x 2) - √(5 x 5 x 3)
= 3 √3 + √105 + 3 x 2 √3 - 5 √3
= 3 √3 + √105 + 6 √3 - 5 √3
= (3 + 6 - 5) √3 + √105
= 4 √3 + √105
Now let us look at the the next problem on "Properties of radicals worksheet".
Problem 6 :
Simplify the following radical expression
√45 + 3 √20 + √80 - 4 √40
Solution :
= √45 + 3 √20 + √80 - 4 √40
First we have to split the given numbers inside the radical as much as possible.
= √(3 x 3 x 5) + √(2 x 2 x 5) +
√(5 x 2 x 2 x 2 x 2) - √(5 x 2 x 2 x 2)
= 3 √5 + 2 √5 + 2 x 2 √5 - 2 √(2 x 5)
= 3 √5 + 2 √5 + 4 √5 - 2 √10
= (3 + 2 + 4) √5 - 2 √10
= 9 √5 - 2 √10
Now let us look at the the next problem on "Properties of radicals worksheet".
Problem 7 :
Simplify the following radical expression
3√5 + 2√95 + 3√117 - √78
Solution :
= 3 √5 + 2√95 + 3√117 - √78
First we have to split the given numbers inside the radical as much as possible
= 3 √5 + 2 √(5 x 19) + 3 √(3 x 3 x 13) - √(3 x 2 x 13)
= 3 √5 + 2 √95 + 3 x 3 √13 - √78
= 3 √5 + 2 √95 + 9 √13 - √78
Now let us look at the the next problem on "Properties of radicals worksheet".
Problem 8 :
Simplify the following radical expression
3 √32 - 2√8 + √50
Solution:
= 3 √32 - 2 √8 + √50
First we have to split the given numbers inside the radical as much as possible.
= 3 √(2 x 2 x 2 x 2 x 2) - 2 √(2 x 2 x 2) + √(5 x 5 x 2)
= (3 x 2 x 2 )√2 - (2 x 2) √2 + 5 √2
= 12 √2 - 4 √2 + 5 √2
= (12 + 5 - 4) √2
= 13 √2
Now let us look at the the next problem on "Properties of radicals worksheet".
Problem 9 :
Simplify the following radical expression
2 √12 - 3√27 - √243
Solution :
= 2 √12 - 3 √27 - √243
First we have to split the given numbers inside the radical as much as possible.
= 2 √(2 x 2 x 3) - 3 √(3 x 3 x 3) - √(3 x 3 x 3 x 3 x 3)
= (2 x 2) √3 - (3 x 3) √3 - (3 x 3) √3
= 4 √3 - 9 √3 - 9 √3
= ( 4 - 9 - 9 ) √3
= -14 √3
Now let us look at the the next problem on "Properties of radicals worksheet".
Problem 10 :
Simplify the following radical expression
√54 - √2500 - √24
Solution :
= √54 - √2500 - √24
First we have to split the given numbers inside the radical as much as possible.
= √(2 x 3 x 3 x 3)-√(5 x 5 x 5 x 5 x 2 x 2)-√(3 x 2 x 2 x 2)
= 3 √(3 x 2) - (5 x 5 x 2) - (2 x 2) √(2 x 3)
= 3 √6 - 50 - 4 √6
= (3 - 4) √6 - 50
= -√6 - 50
Problem 11 :
Simplify the following radical expression
√45 - √25 - √80
Solution :
= √(5 x 3 x 3) - √(5 x 5) - √(5 x 2 x 2 x 2 x 2)
= 3 √5 - 5 - 2 x 2√5
= 3 √5 - 5 - 4√5
= -√5 - 5
Problem 12 :
Simplify the following radical expression
5√95 - 2√50 - 3√180
Solution :
= 5 √95 - 2 √50 - 3 √180
First we have to split the given numbers inside the radical as much as possible.
= 5 √95 - 2 √(2 x 5 x 5) - 3 √(3 x 3 x 2 x 2 x 5)
= 5 √95 - (2 x 5) √2 - (3 x 2 x 3 )√5
= 5 √95 - 10 √2 - 18 √5
Problem 13 :
Solve for "x" :
2√x - 2 = 10
Solution :
2√x - 2 = 10
Add "2" on both sides
2√x = 12
Divide by "2" on both sides
√x = 6
x = 6²
x = 36
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