Square Root Of 1952 In Simplest Radical Form
Simplify the square root of 1952 to its lowest radical form.ANSWER: 4√122
4√122 is in the lowest radical form.
Simplified Radical Form of √1952
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 √1952, we need to divide into factors.
√1952 = √2 x √2 x √2 x √2 x √2 x √61Step 2: List Perfect Squares
1 is a perfect square and divides 1952
4 is a perfect square and divides 1952
16 is a perfect square and divides 1952
Step 3: Divide To Perfect Square
Divide 1952 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 1952 in its simplest form: 4√122
How do you simplify √1952
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 1952. Divide 1952 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 4√122.
Simplified Decimal Form of √1952
The square root of 1952 is approximately 44.181 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √42 | Square root of 42 is the simplest radical form. | √2 x √3 x √7 |
| √47 | Square root of 47 is the simplest radical form. | √47 |
| √23 | Square root of 23 is the simplest radical form. | √23 |
| √107 | Square root of 107 is the simplest radical form. | √107 |
| √434 | Square root of 434 is the simplest radical form. | √2 x √7 x √31 |
| √238 | Square root of 238 is the simplest radical form. | √2 x √7 x √17 |
| √6593 | Square root of 6593 is the simplest radical form. | √19 x √347 |
| √2618 | Square root of 2618 is the simplest radical form. | √2 x √7 x √11 x √17 |
| √6978 | Square root of 6978 is the simplest radical form. | √2 x √3 x √1163 |