Square Root Of 7974 In Simplest Radical Form
Simplify the square root of 7974 to its lowest radical form.ANSWER: 3√886
3√886 is in the lowest radical form.
Simplified Radical Form of √7974
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 √7974, we need to divide into factors.
√7974 = √2 x √3 x √3 x √443Step 2: List Perfect Squares
1 is a perfect square and divides 7974
9 is a perfect square and divides 7974
Step 3: Divide To Perfect Square
Divide 7974 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 7974 in its simplest form: 3√886
How do you simplify √7974
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 7974. Divide 7974 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 3√886.
Simplified Decimal Form of √7974
The square root of 7974 is approximately 89.297 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√6 | Square root of 6 is the simplest radical form. | √2 x √3 |
√87 | Square root of 87 is the simplest radical form. | √3 x √29 |
√10 | Square root of 10 is the simplest radical form. | √2 x √5 |
√525 | 5√21 | √3 x √5 x √5 x √7 |
√137 | Square root of 137 is the simplest radical form. | √137 |
√517 | Square root of 517 is the simplest radical form. | √11 x √47 |
√3765 | Square root of 3765 is the simplest radical form. | √3 x √5 x √251 |
√2386 | Square root of 2386 is the simplest radical form. | √2 x √1193 |
√4704 | 28√6 | √2 x √2 x √2 x √2 x √2 x √3 x √7 x √7 |