RÁPIDO e FÁCIL | RAIZ QUADRADA EXATA

Summary

In this video, the presenter explains how to solve square roots, starting with the basics of square root notation and progressing to examples with larger numbers. The process involves recognizing perfect squares, performing factorization, and applying properties like the square root of a product. The tutorial covers both simple and complex examples, such as √25, √81, √49, and √144, with the aim of helping viewers understand how to solve square roots step-by-step. Viewers are encouraged to practice and share the video for further learning.

Takeaways

• 😀 Understanding the radical symbol: The square root symbol (√) represents the root, with the number inside being the radicand and the index typically being 2 for square roots.
• 😀 Square roots involve finding a number that, when multiplied by itself, equals the radicand (e.g., √25 = 5, because 5 x 5 = 25).
• 😀 Square roots can be solved quickly for small perfect squares like √9 = 3 and √25 = 5 by recognizing simple multiplication.
• 😀 Factorization is helpful for solving square roots of larger numbers, like √81, by breaking down the number into its prime factors (81 = 3 x 3 x 3 x 3, so √81 = 9).
• 😀 For square roots like √49, you can use the basic rule of pairs—every pair of identical factors 'comes out' of the square root (√49 = 7).
• 😀 For numbers that aren't perfect squares, factorization allows you to break them into manageable parts (e.g., √4900 = √49 × √100 = 7 x 10 = 70).
• 😀 A trick to handle square roots near rounded numbers: Find a number whose square is close to the radicand and adjust up or down as needed (e.g., √441 ≈ 21).
• 😀 Using a product close to 400 (like 20 x 20 = 400) helps estimate square roots for numbers near 400, refining the guess with nearby perfect squares (e.g., √441 = 21).
• 😀 The factorization method simplifies even larger square roots: split the radicand into smaller numbers, find their roots, then multiply the results (e.g., √144 = 12 by factoring it into pairs).
• 😀 The key to mastering square roots is practice: start with simple examples and gradually move to more complex ones while applying factorization for tough cases.

Q & A

What is the symbol used to represent the square root in mathematical notation?

The symbol used to represent the square root is called the 'radical'. The number inside the radical is called the 'radicand', and the index is 2, though it's often not written explicitly, as it is understood to be a square root.

Why is the square root of 25 equal to 5?

The square root of 25 is 5 because 5 multiplied by 5 equals 25. The square root asks for a number that, when multiplied by itself, gives the radicand (the number under the radical).

How do you find the square root of a number when it's not a perfect square?

For numbers that are not perfect squares, you can use factorization. For example, to find the square root of 81, you can break it down into its prime factors (81 = 3 x 3 x 3 x 3). Since there are two pairs of 3's, one 3 comes out of the square root, and the square root of 81 is 9.

What is the method to calculate the square root of large numbers?

To calculate the square root of large numbers, you can use factorization. For example, the square root of 81 is calculated by breaking it into smaller factors (81 = 3 x 3 x 3 x 3) and pairing up the factors. One number from each pair comes out of the square root, giving you the answer.

How can you find the square root of 4900?

To find the square root of 4900, break it into smaller factors. You can express it as 49 x 100. The square root of 49 is 7, and the square root of 100 is 10. Multiply 7 by 10 to get the square root of 4900, which is 70.

What is the shortcut for finding the square root of 144?

The shortcut for finding the square root of 144 is to factor it. First, divide 144 by 2 repeatedly: 144 ÷ 2 = 72, 72 ÷ 2 = 36, 36 ÷ 2 = 18, 18 ÷ 2 = 9, then factor 9 into 3 x 3. Each pair of equal factors (like 2's and 3's) brings one number out of the square root. So, 2 x 2 x 3 = 12, and the square root of 144 is 12.

What is the square root of 441, and how can you calculate it quickly?

The square root of 441 is 21. A quick way to find it is by considering a nearby perfect square like 400 (20 x 20). Since 441 is a little larger than 400, test 21 x 21, which equals 441. This method involves estimating based on nearby squares.

Can you always calculate square roots by just factoring the number?

Factoring is a helpful method for finding square roots of perfect squares, but for non-perfect squares, you may need a calculator or other numerical methods. Factoring works well for numbers with easily identifiable prime factors.

What does the phrase 'A cada dois iguais um sai da raiz' mean in the context of square roots?

'A cada dois iguais um sai da raiz' means that for every two identical factors in the factorization of a number, one of them can be taken out of the square root. For example, with 144, the factors are 2 x 2 x 2 x 2 x 3 x 3, and two 2's and two 3's come out, resulting in 12.

What should you do if you have trouble calculating a square root in your head?

If you have difficulty calculating a square root in your head, you can use the method of factorization. Break the number into prime factors and group identical ones. For example, for 81, you factor it into 3 x 3 x 3 x 3, and each pair of 3's comes out, giving the square root as 9.