Topic Content:
- Square Root of Numbers
Given the square of these numbers find the square root:
a. 4 × 4 = 16, The square root of 16 is written as \(\scriptsize \sqrt{16}= 4\)
b. 5 × 5 = 25, The square root of 25, \(\scriptsize \sqrt{25}= 5\)
c. 3 × 3 = 9, The square root of 9 , \(\scriptsize \sqrt{9}= 3\)
This implies that the square root of a given number is that number that multiplies itself to give the given number.
Similarly,
d. -4 × -4 = 16, The square root of \(\scriptsize \sqrt{16}= 4\)
e. -5 × -5 = 25, The square root of 25, \(\scriptsize \sqrt{25}= 5\)
In general, a number has two square roots: one negative square root and one positive square root.
e.g. \(\scriptsize \sqrt{16} \\ \scriptsize = \sqrt{4 \: \times \: 4}\\ \scriptsize = \sqrt{-4 \: \times \: -4} \\ \scriptsize = \pm{4}\)
\(\scriptsize \sqrt{25} \\ \scriptsize = \sqrt{5 \: \times \: 5}\\ \scriptsize = \sqrt{-5 \: \times \: -5}\\ \scriptsize = \pm{5} \)Worked Example 2.2.1:
Find the square root of
a. 144
b. 81
c. 324
d. 900
Solution
a. Square root of 144 = \(\scriptsize \sqrt{144}\)
Step 1: Express 144 as product of prime factors.
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