how to find square root of a 2 digit as well 3 digit no.
Answers
Answer:
While finding the square roots of perfect squares between 100 and 10000, occasionally some anomalous situations arise, and we have to rule out the incorrect one.
Ex.1: Find the square root of 324.
Answer: Concentrate on 3 leaving out the 24. Since 12<3<22, the tenths place number in square root is 1. The unit digit in the square root to give 4 as ending digit in the square can be 2 or 8.
So, we have two choices, 12 and 18, and digital sum of the square is 9 or 0, and so is the case with the squares of 12 and 18. So, the number in the tenths digit of the square will have to come to the rescue.
If we choose 12, the number in the tenths digit of the square root will be
1x2 + 1x 2 = 4 which is not so in the square.
If we choose 18, then the number in the tenths digit of the root will be found from: ……. 1x8 + 1x 8 =16 8x8 =64. so that the number in the tenths digit becomes 16 + 6 ending in 2 in that place Hence, 18 is the required square root.
Ex.2: Find the square root of 484.
Answer: Concentrate on 4, leaving out 84. So, 2 has to be in the tenths place of the square root. The square ends in 4, and so the square root has to end in 2 or 8.
The digital sum of 484 is 7. The digital sum of 22 x 22 is 4 x 4, which is 7.
The digital sum of 28 x 28 = 1 x 1 = 1, and hence 28 is ruled out.
The correct square root is therefore 22.
Answer:
2
Find the value of (29)³ by the short-cut method. Solution: Here, a = 2 and b =9. a² × a = a³; a² × 3b = 3a² × b; b² × 3a = 3a × b²; b² × b = b³ Therefore, (29)³ = 24389.