ROOTS OF INTEGERS WORKSHEET
About "Roots of integers worksheet"
Roots of integers worksheet :
Here we are going to see some practice questions of the topic roots of integers.
Roots of integers worksheet - Practice questions
(1) Find the real number root of √64
(2) Find the real number root of ∛512
(3) Find the real number root of ∛-8000
(4) Find the real number root of ∜16
Question 1 :
Find the real number root of √64
Solution :
Step 1 :
Index of the given square root = 2
Let "x" be the required root
x = √64
Step 2 :
In order to remove the square root, take squares on both sides
x² = (√64)²
x² = 64
Step 3 :
Express 64 as the product of two same numbers
That is, 64 = 8 x 8
64 = 8²
x² = 8²
Step 4 :
Since the powers are equal, then their base are also equal.
x = 8
Hence the required root is 8.
Question 2 :
Find the real number root of ∛512
Solution :
Step 1 :
Index of the given square root = 3
Let "x" be the required root
x = ∛512
Step 2 :
In order to remove the square root, raise power 3 on both sides
x³ = (∛512)³
x³ = 512
Step 3 :
Express 512 as the product of two same numbers
That is, 512 = 8 x 8 x 8
512 = 8³
x³ = 8³
Step 4 :
Since the powers are equal, then their base are also equal.
x = 8
Hence the required root is 8.
Question 3 :
Find the real number root of ∛-8000
Solution :
Step 1 :
Index of the given square root = 3
Let "x" be the required root
x = ∛-8000
Step 2 :
In order to remove the square root, raise power 3 on both sides
x³ = (∛-8000)³
x³ = -8000
Step 3 :
Express -8000 as the product of two same numbers
That is, -8000 = (-20) x (-20) x (-20)
-8000 = (-20)³
x³ = (-20)³
Step 4 :
Since the powers are equal, then their base are also equal.
x = -20
Hence the required root is -20.
Question 4 :
Find the real number root of ∜16
Solution :
Step 1 :
Index of the given square root = 4
Let "x" be the required root
x = ∜16
Step 2 :
In order to remove the square root, raise power 3 on both sides
x⁴ = (∜16)⁴
x⁴ = 16
Step 3 :
Express 16 as the product of two same numbers
That is, 16 = 2 x 2 x 2 x 2
16 = 2⁴
x⁴ = 2⁴
Step 4 :
Since the powers are equal, then their base are also equal.
x = 2
Hence the required root is 2.
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