Square Root Of 4 In Simplest Radical Form
Simplify the square root of 4 to its lowest radical form.ANSWER: 2√1
2√1 is in the lowest radical form.
Simplified Radical Form of √4
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 √4, we need to divide into factors.
√4 = √2 x √2Step 2: List Perfect Squares
1 is a perfect square and divides 4
4 is a perfect square and divides 4
Step 3: Divide To Perfect Square
Divide 4 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 4 in its simplest form: 2√1
How do you simplify √4
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 4. Divide 4 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 2√1.
Simplified Decimal Form of √4
The square root of 4 is approximately 2 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√77 | Square root of 77 is the simplest radical form. | √7 x √11 |
√81 | 9√1 | √3 x √3 x √3 x √3 |
√19 | Square root of 19 is the simplest radical form. | √19 |
√573 | Square root of 573 is the simplest radical form. | √3 x √191 |
√830 | Square root of 830 is the simplest radical form. | √2 x √5 x √83 |
√257 | Square root of 257 is the simplest radical form. | √257 |
√7144 | 2√1786 | √2 x √2 x √2 x √19 x √47 |
√3868 | 2√967 | √2 x √2 x √967 |
√3146 | 11√26 | √2 x √11 x √11 x √13 |