Square Root Of 7 In Simplest Radical Form

Simplify the square root of 7 to its lowest radical form.

ANSWER: Square root of 7 is the simplest radical form.

Square root of 7 is the simplest radical form. is in the lowest radical form.

Simplified Radical Form of √7

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 √7, we need to divide into factors.

√7 = √7

Step 2: List Perfect Squares

1 is a perfect square and divides 7

Step 3: Divide To Perfect Square

Divide 7 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 7 in its simplest form: Square root of 7 is the simplest radical form.

How do you simplify √7

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 7. Divide 7 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 Square root of 7 is the simplest radical form..

Simplified Decimal Form of √7

The square root of 7 is approximately 2.646 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√40 2√10 √2 x √2 x √2 x √5
√39 Square root of 39 is the simplest radical form. √3 x √13
√86 Square root of 86 is the simplest radical form. √2 x √43
√806 Square root of 806 is the simplest radical form. √2 x √13 x √31
√324 18√1 √2 x √2 x √3 x √3 x √3 x √3
√552 2√138 √2 x √2 x √2 x √3 x √23
√8957 13√53 √13 x √13 x √53
√6153 Square root of 6153 is the simplest radical form. √3 x √7 x √293
√8717 Square root of 8717 is the simplest radical form. √23 x √379

Convert any root forms to simplest radical form.

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