A day full of math games & activities. Find one near you.

Square Root of 1500

The square root of 1500 is expressed as √1500 in the radical form and as (1500)^½ or (1500)^0.5 in the exponent form. The square root of 1500 rounded up to 5 decimal places is 38.72983. It is the positive solution of the equation x² = 1500. We can express the square root of 1500 in its lowest radical form as 10 √15.

Square Root of 1500: 38.72983346207417
Square Root of 1500 in exponential form: (1500)^½ or (1500)^0.5
Square Root of 1500 in radical form: √1500 or 10 √15

Square Root of 1500

1.	What is the Square Root of 1500?
2.	How to find the Square Root of 1500?
3.	Is the Square Root of 1500 Irrational?
4.	FAQs

What is the Square Root of 1500?

The square root of 1500, (or root 1500), is the number which when multiplied by itself gives the product as 1500. Therefore, the square root of 1500 = √1500 = 10 √15 = 38.72983346207417.

☛ Check: Square Root Calculator

How to Find Square Root of 1500?

Square Root of 1500 by Long Division Method

Value of √1500 by Long Division Method

Explanation:

Forming pairs: 15 and 00
Find a number Y (3) such that whose square is <= 15. Now divide 15 by 3 with quotient as 3.
Bring down the next pair 00, to the right of the remainder 6. The new dividend is now 600.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 8) such that 6Z × Z <= 600. After finding Z, together 6 and Z (8) form a new divisor 68 for the new dividend 600.
Divide 600 by 68 with the quotient as 8, giving the remainder = 600 - 68 × 8 = 600 - 544 = 56.
Now, let's find the decimal places after the quotient 38.
Bring down 00 to the right of this remainder 56. The new dividend is now 5600.
Add the last digit of quotient to divisor i.e. 8 + 68 = 76. To the right of 76, find a digit Z (which is 7) such that 76Z × Z <= 5600. Together they form a new divisor (767) for the new dividend (5600).
Divide 5600 by 767 with the quotient as 7, giving the remainder = 5600 - 767 × 7 = 5600 - 5369 = 231.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1500.

Therefore, the square root of 1500 by long division method is 38.7 approx.

Is Square Root of 1500 Irrational?

The actual value of √1500 is undetermined. The value of √1500 up to 25 decimal places is 38.72983346207416885179265. Hence, the square root of 1500 is an irrational number.

☛ Also Check:

Square Root of 729 - √729 = 27
Square Root of 108 - √108 = 10.39230
Square Root of 106 - √106 = 10.29563
Square Root of 48 - √48 = 6.92820
Square Root of 1000 - √1000 = 31.62278
Square Root of 250 - √250 = 15.81139
Square Root of 98 - √98 = 9.89949

Square Root of 1500 Solved Examples

Example 1: Solve the equation x² − 1500 = 0

Solution:

x² - 1500 = 0 i.e. x² = 1500
x = ±√1500
Since the value of the square root of 1500 is 38.730,
⇒ x = +√1500 or -√1500 = 38.730 or -38.730.
Example 2: If the area of an equilateral triangle is 1500√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 1500√3 in²
⇒ a = ±√6000 in
Since length can't be negative,
⇒ a = √6000 = 2 √1500
We know that the square root of 1500 is 38.730.
⇒ a = 77.460 in
Example 3: If the surface area of a sphere is 6000π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 6000π in²
⇒ r = ±√1500 in
Since radius can't be negative,
⇒ r = √1500
The square root of 1500 is 38.730.
⇒ r = 38.730 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 1500

What is the Value of the Square Root of 1500?

The square root of 1500 is 38.72983.

Why is the Square Root of 1500 an Irrational Number?

Upon prime factorizing 1500 i.e. 2² × 3¹ × 5³, 3 is in odd power. Therefore, the square root of 1500 is irrational.

What is the Value of 8 square root 1500?

The square root of 1500 is 38.730. Therefore, 8 √1500 = 8 × 38.730 = 309.839.

What is the Square of the Square Root of 1500?

The square of the square root of 1500 is the number 1500 itself i.e. (√1500)² = (1500)^2/2 = 1500.

If the Square Root of 1500 is 38.730. Find the Value of the Square Root of 15.

Let us represent √15 in p/q form i.e. √(1500/100) = 15/10 = 3.873. Hence, the value of √15.0 = 3.873

What is the Square Root of 1500 in Simplest Radical Form?

We need to express 1500 as the product of its prime factors i.e. 1500 = 2 × 2 × 3 × 5 × 5 × 5. Therefore, √1500 = √2 × 2 × 3 × 5 × 5 × 5 = 10 √15. Thus, the square root of 1500 in the lowest radical form is 10 √15.

Math worksheets and
visual curriculum