compute the squares of natural numbers from 90 to 100
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Answers
answer
90 8100
91 8281
92 8464
93 8649
94 8836
95 9025
96 9216
97 9409
98 9604
99 9801
100 10000
The squares of natural numbers from 90 to 100 are 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801,10000
Given:
Natural numbers from 90 to 100
To find:
Compute the squares of natural numbers from 90 to 100
Solution:
In general we can compute squares of the numbers by multiplying given number two times
Example: square of 2 = 2 × 2 = 4
But it will difficult to calculate when it comes to two digit number
To calculate the squares of two digit numbers like 98, 96 .. etc.
we will use the following algebraic identities
(a + b)² = a² + b² +2ab
(a - b)² = a² + b² - 2ab
Given numbers Natural numbers from 90 to 100
⇒ 90 × 90 = 8100
⇒ 100 × 100 = 10000
91×91= (90+1) (90+1) = (90+1)²
= 90² + 1² +2(90)1 = 8100+1+180= 8281
92×92 = (90+2)²
= 90² + 2² +2(90)2 = 8100+1+360= 8464
93×93= (90+3)²
= 90² + 3² +2(90)3 = 8100+9+540= 8649
94×94= (90+4)²
= 90² + 4² +2(90)4 = 8100+16 +720 = 8836
95×95= (90+5)²
= 90² + 5² +2(90)5 = 8100+25+900 = 9025
96×96= (90+6)²
= 90² + 6² +2(90)6 = 8100+36+1080 = 9216
97×97 = (100-3)²
=100² + 3² - 2(100)3 = 10000 + 9 - 600 = 9409
98×98 = (100-2)²
= 100² + 2² +2(100)2 = 10000 + 4 - 400 = 9604
99×99 = (90+1)²
= 100² + 1² +2(100)1 = 10000 + 1 - 200 = 9801
Therefore,
The squares of natural numbers from 90 to 100 are
8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801,10000
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