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15 June, 01:29

Find the possible ones place digit in the square root of the following (apply the properties) a) 2039184

b) 10,004,569

How many natural numbers lie between the squares of 41 and 42?

What will be the value of ' x' in Pythagorean triplet (41, 9, x) ?

Check whether 15028 is a perfect square? If not find the smallest number by which 15028 be divided to make it a perfect square. Also find the square root of the new number formed.

A gardener has 5190 plants. He wants to plant in such a way that the number of rows and columns remains the same. Find the minimum number of plants left in this arrangement.

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  1. 15 June, 04:26
    0
    The answer is given below

    Step-by-step explanation:

    1) Find the possible ones place digit in the square root of the following

    a) 2039184

    The number 2039184 ends with 4, therefore the square root of the number can either end in 2 or 8

    2² = 4, √4 = 2

    8² = 64, √64 = 8

    b) 10,004,569

    The number 10,004,569 ends with 9, therefore the square root is the number will end in 3

    3² = 9, √9 = 3

    2) How many natural numbers lie between the squares of 41 and 42

    42² = 1764 and 41² = 1681

    Therefore the numbers that lie between 1764 and 1681 = (1764 - 1681) - 1 = 83 - 1 = 82

    3) What will be the value of ' x' in Pythagorean triplet (41, 9, x)

    Pythagorean consist of three positive numbers a, b, c such that a² + b² = c². Therefore: x² + 9² = 41²

    x² = 41² - 9² = 1681 - 81

    x² = 1600

    x = √1600 = 40

    4) Check whether 15028 is a perfect square

    15028 = 2 * 2 * 13 * 17 * 17

    15028 = 2² * 13 * 17²

    It is not a perfect square. If it is divided by 13 it becomes a perfect square, that is:

    15028/13 = 2² * 17²

    15028/13 = (2 * 17) ² = 34²

    34² = 15028/13

    34² = 1156

    The square root of the new number formed is 34 (i. e √1156)

    5) A gardener has 5190 plants. He wants to plant in such a way that the number of rows and columns remains the same.

    let the number if rows be x. Since the rows and columns are the same, the number of columns = x.

    x² = 5190

    x = √5190 = 72² + 6.

    Therefore at least six plant would be left out
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