SQUARE ROOTS AND CUBE ROOTS
IMPORTANT FACTS AND FORMULAE
Square Root:
If x
2
=
y,
we say that the square root of
y
is x and we write, √y
=
x.
Thus, √4 = 2, √9 = 3, √196 = 14.
Cube Root:
The cube root of a given number x is the number whose cube is x. We
denote the cube root of x by
3
√x.
Thus,
3
√8
=
3
√2 x 2 x 2 = 2,
3
√343 =
3
√7 x 7 x 7 = 7 etc.
Note:
1.√xy = √x * √y
2. √(x/y) = √x / √y
= (√x / √y) * (√y / √y) = √xy / y
SOLVED EXAMPLES
Ex. 1. Evaluate √6084 by factorization method .
Sol.
Method:
Express the given number as the product of prime factors.
2
6084
Now, take the product of these prime factors choosing one out of
2
3042
every pair of the same primes. This product gives the square root
3
1521
of the given number.
3
507
Thus, resolving 6084 into prime factors, we get:
13
169
6084 = 2
2
x 3
2
x 13
2
13
∴
√
6084
= (2 x 3 x 13) = 78.
Ex. 2. Find the square root of 1471369.
Sol.
Explanation:
In the given number, mark off the digits
1
1471369 (1213
in pairs starting from the unit's digit. Each pair and
1
the remaining one digit is called a period.
22
47
Now, 1
2
= 1. On subtracting, we get 0 as remainder.
44
Now, bring down the next period
i.e.,
47.
241
313
Now, trial divisor is 1 x 2 = 2 and trial dividend is 47.
241
So, we take 22 as divisor and put 2 as quotient.
2423
7269
The remainder is 3.
7269
Next, we bring down the next period which is 13.
x
Now, trial divisor is 12 x 2 = 24 and trial dividend is
313. So, we take 241 as dividend and 1 as quotient.
The remainder is 72.
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 Spring '11
 vinh
 Square number, Ex.

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