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Is 529 a perfect square?
Yes because 232 = 529
What is the perfect square of 23?
529
The only perfect square between 100 and 1000?
There is more than one perfect square between 100 and 1000! All the perfect squares between those two numbers: 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961.
What is the volume of a cuboid when its height is in the ratio of 15 to 8 to its width and has a length of 22 cm with a surface area of 2506 square cm showing work?
Suppose the height is 15x cm. Then the width is 8x cm. Then the surface area is 2*(15x*8x + 8x*22 + 22*15x) cm2 Therefore 2*(15x*8x + 8x*22 + 22*15x) = 2506 or 15x*8x + 8x*22 + 22*15x = 1253 120x2 + 506x - 1253 = 0 so that x = -529/30 or 13/4 But x cannot be negative so x = 1.75. Therefore, volume = (15*1.75)*(8*1.75)*22 = 8085 cm3
How can you rewrite a perfect square as a exponent?
Find its square root and raise it in the second power.64 = 8281 = 92841 = ?2 you need to work a little bit here1. base would be in two digits (odd number with 3 digits, (3+1)/2)2. the first digit would be 2 (the square of 2 is less than 8), so the base would be between 20 and 30.3. the second digit would be 9 (the square of 9 ends in 1)4. the answer is 29, 841 = 292529 = ?21. base would be in two digits (odd number with 3 digits, (3+1)/2)2. the first digit would be 2 (the square of 2 is less than 5), so the base would be between 20 and 30.3. the second digit would be 3 or 7 (the square of 3 and 7 end in 9); is it 23 or 27?4. 529 - 2232 = 529 - 409 = 120; it is 3, because 2(2*3)=12. So 529 = 2322809 = ?21. base would be in two digits (even number with 4 digits, 4/2)2. the first digit would be 5 (the square of 5 is less than 28,), so the base would be between 50 and 60.3. the second digit would be 3 or 7 (the square of 3 and 7 end in 9); is it 53 or 57?4. 2809 - 5232 = 2809 - 2509 = 300; it is 3, because 2(5*3)=30. So 2809 = 5327056 = ?21. base would be in two digits (even number with 4 digits, 4/2)2. the first digit would be 8 (the square of 8 is less than 70,), so the base would be between 80 and 90.3. the second digit would be 4 or 6 (the square of 4 and 6 end in 6); is it 84 or 86?4. 7056 - 8242 = 7056 - 6416 = 640; it is 4, because 2(8*4)=64. So 7056 = 8427396 = ?21. base would be in two digits (even number with 4 digits, 4/2)2. the first digit would be 8 (the square of 8 is less than 73), so the base would be between 80 and 90.3. the second digit would be 4 or 6 (the square of 4 and 6 end in 6); is it 84 or 86?4. 7396 - 8262 = 7396 - 6436 = 960; it is 6, because 2(8*6)=96. So 7396(if you test 4 first, you'll see that it doesn't work, so it will be 6)55696 = ?21. base would be in three digits (odd number with 5 digits, (5+1)/2)2. the first digit would be 2 (the square of 2 is less than 5), so the base would be between 200 and 300.3. the last digit would be 4 or 6 (the square of 4 and 6 end in 6); is it 2_4 or 2_6?4. let's work a little bit here:2_4; 22_42 = 4001640016+ ... = 4569600080 (101*2*4*_, we need to find the middle digit)01600 (102*2*2*4)04000 (103*2*2*_)55696 - 45696 = 10000400160008001600040001000000080 doesn't change, this tell us the middle digit can be 1 or 6. But one is too small and 6 is too big (2*2*1= 4, 2*2*6=32). So the last digit is not 4, it is 6. Let's find the middle digit.2_6; 22_62 = 4003640036+ ... = 4655600120 (101*2*6*_, we need to find the middle digit)02400 (102*2*2*6)04000 (103*2*2*_)55696 - 46556 = 9140400360012002400040000914000120 becomes 00160, and tell us the middle digit can be 3 or 8, but 8 is too big (2*2*8=32), so it is 3Thus, 55696 = 2362.263169 = ?21. base would be in three digits (even number with 6 digits, 6/2)2. the first digit would be 5 (the square of 5 is less than 26), so the base would be between 500 and 600.3. the second digit would be 3 or 7 (the square of 3 and 7 end in 9); is it 5_3 or 5_7?4. let's work a little bit here:5_3; 52_32 = 250009250009+ ... = 263069000060 (101*2*3*_, we need to find the middle digit)003000 (102*2*5*3)010000 (103*2*5*_)263169 - 263069 = 10025000900006000300001000000010000060 doesn't change so the only possibility is when the middle digit is 1.Thus, 2631169 = 5132
