Square Root Of 47 In Simplest Radical Form

Simplify the square root of 47 to its lowest radical form.

ANSWER: Square root of 47 is the simplest radical form.

Square root of 47 is the simplest radical form. is in the lowest radical form.

Simplified Radical Form of √47

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 √47, we need to divide into factors.

√47 = √47

Step 2: List Perfect Squares

1 is a perfect square and divides 47

Step 3: Divide To Perfect Square

Divide 47 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 47 in its simplest form: Square root of 47 is the simplest radical form.

How do you simplify √47

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 47. Divide 47 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 47 is the simplest radical form..

Simplified Decimal Form of √47

The square root of 47 is approximately 6.856 when expressed in decimal form and you can find additive inverse of a decimal number.

Calculation Table:

Square Root Answer Calculation
√70 Square root of 70 is the simplest radical form. √2 x √5 x √7
√30 Square root of 30 is the simplest radical form. √2 x √3 x √5
√79 Square root of 79 is the simplest radical form. √79
√413 Square root of 413 is the simplest radical form. √7 x √59
√195 Square root of 195 is the simplest radical form. √3 x √5 x √13
√910 Square root of 910 is the simplest radical form. √2 x √5 x √7 x √13
√9610 31√10 √2 x √5 x √31 x √31
√5601 Square root of 5601 is the simplest radical form. √3 x √1867
√9178 Square root of 9178 is the simplest radical form. √2 x √13 x √353

Convert any root forms to simplest radical form.

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