What are the Different Square Roots of 49?

The square root of 49 has two different values, a positive and a negative value. Here’s a table showing the different square roots of 49:

Type of Square Root	Value
Positive Square Root	7
Negative Square Root	-7

The square root of 49 is 7 or -7 because 7 * 7 = 49 and (-7) * (-7) = 49.

What are the Different Square Roots of 49?

The square root of 49 has two different values: the positive square root, which is 7, and the negative square root, which is -7. Both 7 and -7, when squared, result in 49, making them the two different square roots of 49.

Square roots involve finding which number, when multiplied by itself, equals the given number. For example, 4 is a square root of 16 because 4 x 4 = 16. Numbers can have multiple square roots, depending on whether they are perfect squares. In this post, we’ll find all the square roots of the number 49 and discuss strategies for identifying square roots. We’ll also look at interesting properties of square numbers and the significance of square roots in mathematics.

Understanding Square Roots

Let’s start with some basics about square roots. The main square root notation is the radical sign √ preceding a number. For example:

√16 = 4 because 4 x 4 = 16 √9 = 3 because 3 x 3 = 9

The √ symbol means to find which number times itself equals the number inside. To be a valid square root, the number under the radical must be a perfect square. Perfect squares are numbers like 4, 9, 16 and 36 that have integer square roots. Non-perfect squares like 50 do not have integer square roots (√50 is irrational).

Finding Square Roots of 49

Now let’s find the square roots of 49. We can either guess and check:

√49 = ? √49 = 7 (7 x 7 = 49, so 7 is a square root)

Or use a calculator to confirm 7 is a square root of 49. But 49 also has another square root: -7.

(-7) x (-7) = 49

So the two square roots of 49 are:

√49 = 7 √49 = -7

This makes sense because 49 is a perfect square, being 7 squared. Perfect squares have both positive and negative roots.

Properties of Square Roots

Here are some other helpful properties when working with square roots:

• For √a x √b = √(ab)
• √(a/b) = √a / √b
• √a + √b ≠ √(a + b) (not equivalent expressions)

Understanding these allows manipulation of square roots following algebraic rules.

Applications of Square Roots

Square roots feature prominently in math and science formulas including:

• The quadratic formula for solving polynomials
• The Pythagorean theorem for right triangle sides
• Equation of a circle needing radius
• Physics equations involving area and volume

Having fluency with square roots enables understanding across quantitative fields.

Conclusion

In this post we determined the two square roots of 49 are 7 and -7. We also reviewed properties and applications of square roots. While a simple example, it demonstrates the logic, notation, and underlying concepts involved in fluency with squares and square roots.

Regular practice with square root problems of increasing complexity helps develop the skills needed to tackle advanced math and science questions.

Whether using the quadratic formula, analyzing geometric shapes, or working with multidimensional figures, square root mastery provides a critical foundation. Each square root solved represents one more building block towards mathematical maturity across disciplines.