Square Root Of 74805201 In Simplest Radical Form
Simplify the square root of 74805201 to its lowest radical form.ANSWER: 8649√1
8649√1 is in the lowest radical form.
Simplified Radical Form of √74805201
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 √74805201, we need to divide into factors.
√74805201 = √3 x √3 x √3 x √3 x √31 x √31 x √31 x √31Step 2: List Perfect Squares
1 is a perfect square and divides 74805201
9 is a perfect square and divides 74805201
81 is a perfect square and divides 74805201
961 is a perfect square and divides 74805201
8649 is a perfect square and divides 74805201
77841 is a perfect square and divides 74805201
923521 is a perfect square and divides 74805201
8311689 is a perfect square and divides 74805201
74805201 is a perfect square and divides 74805201
Step 3: Divide To Perfect Square
Divide 74805201 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 74805201 in its simplest form: 8649√1
How do you simplify √74805201
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 74805201. Divide 74805201 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 8649√1.
Simplified Decimal Form of √74805201
The square root of 74805201 is approximately 8649 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √48 | 4√3 | √2 x √2 x √2 x √2 x √3 |
| √14 | Square root of 14 is the simplest radical form. | √2 x √7 |
| √59 | Square root of 59 is the simplest radical form. | √59 |
| √138 | Square root of 138 is the simplest radical form. | √2 x √3 x √23 |
| √174 | Square root of 174 is the simplest radical form. | √2 x √3 x √29 |
| √359 | Square root of 359 is the simplest radical form. | √359 |
| √4712 | 2√1178 | √2 x √2 x √2 x √19 x √31 |
| √6129 | 3√681 | √3 x √3 x √3 x √227 |
| √3990 | Square root of 3990 is the simplest radical form. | √2 x √3 x √5 x √7 x √19 |