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 and you can find additive inverse of a decimal number.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√58 | Square root of 58 is the simplest radical form. | √2 x √29 |
√67 | Square root of 67 is the simplest radical form. | √67 |
√76 | 2√19 | √2 x √2 x √19 |
√501 | Square root of 501 is the simplest radical form. | √3 x √167 |
√998 | Square root of 998 is the simplest radical form. | √2 x √499 |
√335 | Square root of 335 is the simplest radical form. | √5 x √67 |
√2018 | Square root of 2018 is the simplest radical form. | √2 x √1009 |
√3031 | Square root of 3031 is the simplest radical form. | √7 x √433 |
√8074 | Square root of 8074 is the simplest radical form. | √2 x √11 x √367 |