The Square Root Function Answers

Which mathematical terms originated from the Arabic mathematician, al-Khwarizmi? Check all that apply.algebradecimalfractionperfect squareremainderroot

According to Egyptian artifacts, how early was the concept of the square root known?

The concepts of perfect and nonperfect squares appeared in many ancient texts. Complete the sentences to identify the perfect and nonperfect squares. is a perfect square. is a nonperfect square.

The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of . In order to determine , let G1 = 2, a number whose square is close to 5. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary. Average 2.25 and to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

The Bakhshali Manuscript shows that another method for calculating nonperfect squares was being used in India by 400 CE. Use this method to find the approximate value of . The nearest perfect square that is less than 22 is , whose square root is . Add the square root from step 1 to to get 4.75. Calculate the quantity one-half times the square of divided by the value found in step 2, or 4.75. Subtract the value found in step 3 from the value found in step 2, or 4.75.The approximate value of is .

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