Without actual multiplication, find the square of the following number. 73

To find the square of 73 without performing actual multiplication, we can use the same algebraic identity:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, express 73 as \(a + b\), where \(a = 70\) and \(b = 3\).

Applying the identity:

\[
73^2 = (70 + 3)^2 = 70^2 + 2 \times 70 \times 3 + 3^2
\]

Now, let's calculate each term:

- \(70^2 = 4900\)
- \(2 \times 70 \times 3 = 2 \times 210 = 420\)
- \(3^2 = 9\)

Add these up:

\[
73^2 = 4900 + 420 + 9 = 5329
\]

So, the square of 73 is **5329**.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. What is the square of 83 using a similar method?
2. How can you square 68 without actual multiplication?
3. Can you apply this method to square a number like 125?
4. How does this method compare with the binomial theorem?
5. What is the square of 89 using the identity?

**Tip:** Breaking a number into parts close to multiples of 10 can simplify squaring or other arithmetic operations!

Learn how to find the square of 73 using algebraic identities without performing actual multiplication. This problem demonstrates the application of the binomial theorem and squaring techniques. Suitable for students in Grades 7-9.

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