Square Root Of 49787136 In Simplest Radical Form

Simplify the square root of 49787136 to its lowest radical form.

ANSWER: 7056√1

7056√1 is in the lowest radical form.

Simplified Radical Form of √49787136

One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y

Explanation:

When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.

Step 1: List Factors

To simplify √49787136, we need to divide into factors.

√49787136 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √7 x √7 x √7 x √7

Step 2: List Perfect Squares

1 is a perfect square and divides 49787136
4 is a perfect square and divides 49787136
9 is a perfect square and divides 49787136
16 is a perfect square and divides 49787136
36 is a perfect square and divides 49787136
49 is a perfect square and divides 49787136
64 is a perfect square and divides 49787136
81 is a perfect square and divides 49787136
144 is a perfect square and divides 49787136
196 is a perfect square and divides 49787136
256 is a perfect square and divides 49787136
324 is a perfect square and divides 49787136
441 is a perfect square and divides 49787136
576 is a perfect square and divides 49787136
784 is a perfect square and divides 49787136
1296 is a perfect square and divides 49787136
1764 is a perfect square and divides 49787136
2304 is a perfect square and divides 49787136
2401 is a perfect square and divides 49787136
3136 is a perfect square and divides 49787136
3969 is a perfect square and divides 49787136
5184 is a perfect square and divides 49787136
7056 is a perfect square and divides 49787136
9604 is a perfect square and divides 49787136
12544 is a perfect square and divides 49787136
15876 is a perfect square and divides 49787136
20736 is a perfect square and divides 49787136
21609 is a perfect square and divides 49787136
28224 is a perfect square and divides 49787136
38416 is a perfect square and divides 49787136
63504 is a perfect square and divides 49787136
86436 is a perfect square and divides 49787136
112896 is a perfect square and divides 49787136
153664 is a perfect square and divides 49787136
194481 is a perfect square and divides 49787136
254016 is a perfect square and divides 49787136
345744 is a perfect square and divides 49787136
614656 is a perfect square and divides 49787136
777924 is a perfect square and divides 49787136
1016064 is a perfect square and divides 49787136
1382976 is a perfect square and divides 49787136
3111696 is a perfect square and divides 49787136
5531904 is a perfect square and divides 49787136
12446784 is a perfect square and divides 49787136
49787136 is a perfect square and divides 49787136

Step 3: Divide To Perfect Square

Divide 49787136 by the largest perfect square you found in the previous step:

Step 4: Calculate The Square Root

Calculate the square root of the largest perfect square:

Final Step :

Put Steps 3 and 4 together to get the square root of 49787136 in its simplest form: 7056√1

How do you simplify √49787136

The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.

Find the lowest prime number that can divide 49787136. Divide 49787136 repeatedly using the long division method till you reach 1.

A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.

Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.

So, the answer is 7056√1.

Simplified Decimal Form of √49787136

The square root of 49787136 is approximately 7056 when expressed in decimal form.

Calculation Table: