Square Root Of 7744 In Simplest Radical Form
Simplify the square root of 7744 to its lowest radical form.ANSWER: 88√1
88√1 is in the lowest radical form.
Simplified Radical Form of √7744
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 √7744, we need to divide into factors.
√7744 = √2 x √2 x √2 x √2 x √2 x √2 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 7744
4 is a perfect square and divides 7744
16 is a perfect square and divides 7744
64 is a perfect square and divides 7744
121 is a perfect square and divides 7744
484 is a perfect square and divides 7744
1936 is a perfect square and divides 7744
7744 is a perfect square and divides 7744
Step 3: Divide To Perfect Square
Divide 7744 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 7744 in its simplest form: 88√1
How do you simplify √7744
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 7744. Divide 7744 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 88√1.
Simplified Decimal Form of √7744
The square root of 7744 is approximately 88 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √41 | Square root of 41 is the simplest radical form. | √41 |
| √56 | 2√14 | √2 x √2 x √2 x √7 |
| √80 | 4√5 | √2 x √2 x √2 x √2 x √5 |
| √453 | Square root of 453 is the simplest radical form. | √3 x √151 |
| √592 | 4√37 | √2 x √2 x √2 x √2 x √37 |
| √411 | Square root of 411 is the simplest radical form. | √3 x √137 |
| √1354 | Square root of 1354 is the simplest radical form. | √2 x √677 |
| √5952 | 8√93 | √2 x √2 x √2 x √2 x √2 x √2 x √3 x √31 |
| √5917 | Square root of 5917 is the simplest radical form. | √61 x √97 |