Hippocampus Algebra: Guess and check method

Last time we learned how to multiply radical expressions. Let's take a quick review.

Find the product of the given expressions.

After selecting your answer, click the “Submit” button.

Now, let's move on with today's lesson.

The square root of a number is another number, which when multiplied by itself, produces the original number.

For example: the <EQUATION> is <EQUATION>.

That’s because <EQUATION>.

We already know the square root of some whole numbers that are perfect squares.

What is the square root of 25? Click the “Submit” button after entering your answer.

We know from the multiplication table we learned in elementary school that <EQUATION>.

So, the <EQUATION> is <EQUATION>.

The square root of a whole number that is a perfect square is just another whole number.

Let’s see if you can do some more on your own.

Find the square root of the given number.

Click the “Submit” button after entering your answer.

Finding the square of a whole number that is not a perfect square is more difficult. Consider the <EQUATION>.

Its square root is not <EQUATION>, because <EQUATION>, which is too small.

And its not <EQUATION>, because <EQUATION>, which is too big.

Its square root must be between 3 and 4. Therefore, it’s not a whole number.

One way we can find a value for the <EQUATION> is to use the |B| guess and check method |/B| .

Let’s find a value for the <EQUATION> to three decimal places.

We already guessed 3 and 4. We know the value is between them.

Which of the following should we use as our next guess? Click the “Submit” button after selecting your answer.

Our next guess is 3.5.

The square of 3.5 is 12.25. That’s a little high, but very close.

Let’s guess 3.45, which is a little smaller than our last guess.

This gives 11.90.

This is also close, but a little low.

Next, let’s guess 3.46, which is slightly higher than our last guess.

This gives 11.97. Its slightly low.

For our next guess, let’s use 3.465.

This gives 12.01.

Finally, let’s try 3.464.

This gives 12.00.

Therefore, we have our square root to three decimal places: 3.464

Now, let’s find the <EQUATION>.

We can say that the square root value must be between 5 and 6, because 30 is between 25 and 36.

What is the <EQUATION>? Give the value to three decimal places. Click the “Submit” button after entering your answer.

We find that: <EQUATION> to three decimal places.

Guessing square roots can become tedious, especially for large numbers.

Next time we’ll look at another method for finding square roots.