60 is not a perfect square, so the answer will still include a radical (a square root of some number). We can simplify the square root of any number, though, if the number has any factors that are perfect squares.

Factors of 61 are 1 and 61. Prime factorization of 61 is 1 x 61. Positive factors of 61 are 1 and 61.

For 61, the answer is: yes, 61 is a prime number because it has only two distinct divisors: 1 and itself (61).

The first few of these, already known to the ancient Greeks, are 6, 28, 496, and 8128….Perfect Number Table:

The square root of 61 rounded up to 7 decimal places is 7.8102497….Square Root of 61 in radical form: √61.

The answer is: √63=√32⋅7=√32⋅√7=3√7 .

7.75

Square root of 63 in the radical form is expressed as √63 and in exponent form it is expressed as 631/2. The square root of 63 rounded to 3 decimal places is ±7.937. We can also express the square root of 63 in its lowest radical form as 3√737. Numbers that have a radical symbol in its lowest form are called surds.

7.8

It can be written as 0.61 in decimal form (rounded to 6 decimal places)….Reduce 61/100 to lowest terms

1. Find the GCD (or HCF) of numerator and denominator. GCD of 61 and 100 is 1.
2. 61 ÷ 1100 ÷ 1.
3. Reduced fraction: 61100. Therefore, 61/100 simplified to lowest terms is 61/100.

The square root of 260 rounded up to 8 decimal places is 16.12451550….Square Root of 260.

9.165

Hence, the factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260.

312 is not a perfect square.

We can express the square root of 333 in its lowest radical form as 3 √37….Square Root of 333.

Is 312 a perfect square number? A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 312 is about 17.664. Thus, the square root of 312 is not an integer, and therefore 312 is not a square number.

Factors of 312

• All Factors of 312: 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156 and 312.
• Prime Factors of 312: 2, 3, 13.
• Prime Factorization of 312: 23 × 31 × 131
• Sum of Factors of 312: 840.

Solution: Since, the prime factors of 804 are 2, 3, 67.