The Square Root Function / Assignment

According to Egyptian artifacts, how early was the concept of the square root known? 1850 BCE 1700 BCE 400 CE 830 CE

1850 BCE

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 _________.

16 / 4 / 0.06 / 4.69

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 G1 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 G2 to find G3 = 2.236. 5 ÷ G3 ≈ ________ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

2.5 / 2.222 / 2.236

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

36 / 10

Which mathematical terms originated from the Arabic mathematician, al-Khwarizmi? Check all that apply. algebra decimal fraction perfect square remainder root

algebra / root