Square root of decimal (example) | Numbers and operations | 8th grade | Khan Academy

TL;DR

The equation P squared = 0.81 can be solved by taking the square root of 0.81 and considering both positive and negative solutions for P.

Transcript

• Let's see if we can solve the equation P squared is equal to 0.81. So how could we think about this? Well one thing we could do is we could say, look if P squared is equal to 0.81, another way of expressing this is, that well, that means that P is going to be equal to the positive or negative square root of 0.81. Remember if we just wrote the squ... Read More

Key Insights

• ❎ To solve the equation P squared = 0.81, we can take the square root of 0.81 and consider both positive and negative solutions for P.
• 😥 Multiplying a number with one digit after the decimal point by itself results in a product with two digits after the decimal point.
• 🟪 0.9 squared is equal to 0.81, allowing us to express 0.81 as 0.9 squared in the equation P squared = 0.81.
• 🟪 Writing P as either ±0.9 or as 0.9 or -0.9 satisfies the equation P squared = 0.81.
• ❎ The value of P can be either positive or negative since squaring a negative number still yields a positive value.
• 🟪 By considering the square root of 0.81, we find that P can be ±0.9, solving the equation P squared = 0.81.
• 😑 The equivalence of 0.81 and 0.9 squared allows for the expression of P as either ±0.9 or as 0.9 or -0.9.

Questions & Answers

Q: How can we solve the equation P squared = 0.81?

To solve the equation P squared = 0.81, we can take the square root of 0.81, resulting in two possible solutions for P: ±0.9. This is because squares of negative numbers also yield positive values.

Q: Why does 0.9 squared equal 0.81?

When multiplying 0.9 by itself, we get 0.81. This is because multiplying a number with one digit after the decimal point by itself will produce a product with two digits after the decimal point.

Q: Can we write 0.81 as 0.9 squared?

Yes, 0.81 can be expressed as 0.9 squared. By substituting 0.81 with its equivalent expression, we can solve the equation P squared = 0.81 as P = ±0.9.

Q: Why can we also write P as negative 0.9 squared?

Writing P as negative 0.9 squared is also valid because multiplying two negative numbers yields a positive value. Since we consider the positive and negative square roots of 0.81, either solution will work.

Summary & Key Takeaways

• The equation P squared = 0.81 can be expressed as P = ± √0.81.

• When multiplying a number with one digit after the decimal point by itself, the resulting product will have two digits after the decimal point.

• By taking the square root of 0.81, the possible solutions for P are ±0.9.