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 √2

Step 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

Convert any root forms to simplest radical form.

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