Square Root Of 78074896 In Simplest Radical Form
Simplify the square root of 78074896 to its lowest radical form.ANSWER: 8836√1
8836√1 is in the lowest radical form.
Simplified Radical Form of √78074896
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 √78074896, we need to divide into factors.
√78074896 = √2 x √2 x √2 x √2 x √47 x √47 x √47 x √47Step 2: List Perfect Squares
1 is a perfect square and divides 78074896
4 is a perfect square and divides 78074896
16 is a perfect square and divides 78074896
2209 is a perfect square and divides 78074896
8836 is a perfect square and divides 78074896
35344 is a perfect square and divides 78074896
4879681 is a perfect square and divides 78074896
19518724 is a perfect square and divides 78074896
78074896 is a perfect square and divides 78074896
Step 3: Divide To Perfect Square
Divide 78074896 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 78074896 in its simplest form: 8836√1
How do you simplify √78074896
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 78074896. Divide 78074896 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 8836√1.
Simplified Decimal Form of √78074896
The square root of 78074896 is approximately 8836 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √13 | Square root of 13 is the simplest radical form. | √13 |
| √11 | Square root of 11 is the simplest radical form. | √11 |
| √61 | Square root of 61 is the simplest radical form. | √61 |
| √460 | 2√115 | √2 x √2 x √5 x √23 |
| √611 | Square root of 611 is the simplest radical form. | √13 x √47 |
| √435 | Square root of 435 is the simplest radical form. | √3 x √5 x √29 |
| √3854 | Square root of 3854 is the simplest radical form. | √2 x √41 x √47 |
| √1584 | 12√11 | √2 x √2 x √2 x √2 x √3 x √3 x √11 |
| √6636 | 2√1659 | √2 x √2 x √3 x √7 x √79 |