What is the Value of a 9

The
square root of 9 is equal to 3. It is represented as√9 in radical form and 9^1/2
in exponential grade. When we multiply a number past itself we get the square of the number. The square root of whatsoever number is a value that is multiplied by itself to get the original value. And so, the square root of 9, denotes to reverse of the square of the number 9. If x is the square root of ix then x^two
= nine.

What is Square root of nine?

Square root of 9 is a whole number that is multiplied by itself to get the original number. The actual value of square root of 9 is iii.

√9 = ±three

If we square +3 or -3, the resulting value will exist equal to nine.

• (+3)ⁱⁱ
  = nine
• (-3)^two
  = 9

Note:

Since, the square root of ix results in a whole number, therefore, 9 is a perfect square.

Also, the root of 9 is a rational number, because we tin stand for √nine = ±3 in the course P/Q, such as 3/1.

How to Observe Square Root of ix?

Number 9 is an odd number and not a prime. Prime number numbers take only two factors, i and the number itself. But as we know, ix take three multiple factors, 1, 3 and ix itself. Thus, we tin can write the number 9 in the form of multiple as;

1 × 9 = 9

iii × 3 = 9

9 × ane = 9

You lot know that number 9 is a multiple of three or when 3 is multiplied by itself, nosotros go the number 9. Therefore, we can write the foursquare root of 9 as;

\(\begin{array}{50}\sqrt{9}\finish{array} \)

=

\(\begin{assortment}{l}\sqrt{3 × 3}\terminate{array} \)

=

\(\begin{array}{50}\sqrt{3^2}\stop{array} \)

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

\(\begin{array}{l}\sqrt{9}\end{array} \)

= ±iii

Basically, the square root of a number gives two root values, one with +ve and some other with -ve symbol. Therefore, the value of the foursquare root of 9 tin can be expressed equally +iii and -3 or we tin can say the roots of nine are +iii and -3.

Number 9 is the perfect foursquare equally it fulfils the criteria which we discussed earlier in the introduction.

Square Root of 9 by Long Segmentation Method

Long sectionalisation method is helpful to find the square root of non-perfect squares. Since, 9 is a perfect square, thus, it is very easy to derive its square using partitioning method. Remember the post-obit points:

• nine is a single-digit number, thus its square root will be less than 9
• ix is an odd number, thus it is not divisible past any even number less than 9 (i.e.,two,4,6,eight is rejected)
• Nosotros have to multiply the remainder of the numbers 3, v, and vii with themselves to find the value equal to nine
• Hence, 3 ten 3 = ix
• And then, the foursquare root of 9 is equal to 3

Important Points

• If the number ends with 2, 3, seven and 8, then the number is non a perfect square.
• A perfect square number ends with ane, iv, 5, 6 and 9.
• It is easy to find the square root of a perfect square number as it results in the whole number, whereas imperfect squares outcome in fractional or decimal numbers. Nosotros tin can easily foursquare a number by just multiplying the number to itself but taking the square root of the number is a fiddling complicated, specially in the case of imperfect squares.
• The square 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 will find out the square root of 9 past a simple method, where nine is the radicand.

Related Articles

Video Lessons on Square Roots

Square Root of 9 Solved Examples

Q.1: What is the value of square root of 9/25?

Solution: Finding the root of 9 and 25 individually we have;

√9 = 3

And,

√25 = five

Thus,√(nine/25) = 3/v

Q.2: Find the sum of √9 + 2√49.

Solution: Since,

√9 = iii

√49 = vii

Therefore,

√9 + two√49 = three + two (7) = 3 + 14 = 17

Download BYJU’S – The Learning App and learn to observe the squares and roots of numbers with the assistance of interactive videos.