3.3 Estimating square roots

Long before Pythagoras of Samos was credited for Pythagorean Theorem, people have already noticed how the 3 sides of a right triangle have a relationship. The theorem simply says that the sum of the squares of the two sides of a right triangle will be equal to the square of the hypotenuse. A simple formula to represent which is a2 + b2 = c2, where a and b are the triangle’s sides, and c is the hypotenuse.

In the first part of this chapter, we will discuss all about squares and square roots. We will be able to learn how obtain the set of prime factors that comprises a number. We will be using Prime Factorization, a process by which we list down all the factors of a certain number until we get its prime factors. Through this method, we will also be able to pinpoint numbers that are perfect squares.

For the second part, we will look at the Pythagorean Theorem more thoroughly to understand how to use it. We will be solving for the hypotenuse, or the sides based on the Pythagorean Theorem.

For the third segment, we will be looking into how to estimate a square root since not all square roots would give us whole numbers.

For the fourth part of this chapter, we will then be discussing all about Pythagorean Relationship. Now instead of just solving for the sides of a triangle we will be dealing with more complex problems like using shapes adjacent to the right triangle to solve for the value of a, b, or c.

In the last part of this chapter, we will be looking closely at how to use the Pythagorean Theorem in more real life situations and problems. In no time, you would be ready to solve problems that are related to the Pythagorean Theorem and you can check out the Pythagorean Calculator online if you want to check your answer.

Estimating square roots

To estimate square roots which are not perfect squares without using a calculator, we need to know the perfect square numbers well. We will first put the number inside the square root sign in the middle of a number line, and then find the two closest perfect square numbers on its left and right hand side to make the best estimation.


  • 1.
    Estimate the values to two decimal places. Check the answers with a calculator.
  • 3.
    Alice has baked a square cake that has a top surface area of 335 cm2c{m^2}. She has a rectangular box that has a width of 20 cm and length of 27 cm.
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Estimating square roots

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