The Square Root Of 9

The foursquare root of nine is equal to 3. It is represented as√9 in radical form and 9^i/two in exponential form. When we multiply a number past itself we go the square of the number. The foursquare root of any number is a value that is multiplied by itself to become the original value. Then, the square root of 9, denotes to contrary of the square of the number nine. If x is the square root of nine then x² = 9.

What is Square root of 9?

Foursquare root of 9 is a whole number that is multiplied by itself to get the original number. The bodily value of square root of 9 is 3.

√9 = ±3

If we square +3 or -3, the resulting value will be equal to 9.

(+iii)² = 9
(-3)^two = 9

Notation:

Since, the foursquare root of nine results in a whole number, therefore, 9 is a perfect foursquare.

Too, the root of 9 is a rational number, because we tin can represent √9 = ±3 in the form P/Q, such every bit 3/i.

How to Find Square Root of 9?

Number nine is an odd number and not a prime number. Prime numbers take merely two factors, i and the number itself. But equally nosotros know, 9 have three multiple factors, one, 3 and 9 itself. Thus, we tin can write the number 9 in the form of multiple as;

ane × nine = 9

three × iii = 9

9 × 1 = 9

You know that number ix is a multiple of 3 or when 3 is multiplied by itself, we get the number 9. Therefore, we can write the square root of 9 as;

\(\begin{array}{fifty}\sqrt{9} = \sqrt{3 \times 3}\end{array} \)

\(\begin{array}{fifty}=\sqrt{iii^2}\end{array} \)

The square cancels the foursquare root of a number. Therefore, if we cancel the foursquare root with a square in the above expression, nosotros become,

\(\begin{array}{l}\sqrt{9} = \pm iii\end{array} \)

Basically, the square root of a number gives 2 root values, one with +ve and another with -ve symbol. Therefore, the value of the square root of 9 can exist expressed as +three and -3 or we tin say the roots of 9 are +three and -three.

Number 9 is the perfect square equally it fulfils the criteria which nosotros discussed before in the introduction.

Foursquare Root of ix past Long Division Method

Long division method is helpful to observe the foursquare root of non-perfect squares. Since, nine is a perfect foursquare, thus, it is very easy to derive its foursquare using partitioning method. Think the following points:

9 is a single-digit number, thus its square root will be less than 9
9 is an odd number, thus it is not divisible by any even number less than 9 (i.e.,2,4,6,8 is rejected)
Nosotros accept to multiply the rest of the numbers 3, 5, and 7 with themselves to observe the value equal to 9
Hence, three x 3 = ix
So, the foursquare root of ix is equal to 3

Of import Points

If the number ends with 2, 3, 7 and eight, and so the number is not a perfect square.
A perfect square number ends with 1, 4, v, 6 and 9.
It is easy to find the square root of a perfect square number every bit it results in the whole number, whereas imperfect squares outcome in partial or decimal numbers. We can easily square a number by simply multiplying the number to itself but taking the square root of the number is a little complicated, particularly in the example of imperfect squares.
The foursquare root is represented by '√' symbol. This symbol is named a radical symbol or radix. And the number underneath the radical symbol or radix is called the radicand. Here, we volition detect out the square root of ix by a simple method, where ix is the radicand.

Video Lessons on Foursquare Roots

Visualising square roots

Finding Square roots

Foursquare Root of 9 Solved Examples

Q.one: What is the value of square root of 9/25?

Solution: Finding the root of nine and 25 individually we have;

√nine = 3

And,

√25 = 5

Thus,√(9/25) = iii/5

Q.2: Observe the sum of √9 + 2√49.

Solution: Since,

√ix = 3

√49 = 7

Therefore,

√9 + two√49 = 3 + two (vii) = 3 + xiv = 17

Ofttimes Asked Questions – FAQs

What is actual value of square root of 9?

The value of foursquare root of nine is 3.

Is root 9 a rational or irrational?

Root 9 is a rational number because √9 = 3 tin can be expressed equally 3/ane.

What is the foursquare root of -ix?

The square root of -9 is 3i, since √-1 = i, where i is the imaginary number.

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