Mathematics
Grade-8
Easy
Question
Which of the following can be a perfect square?
- A number ending in 3 or 7
- A number ending with an odd number of zeros
- A number ending with an even number of zeros
- number ending in 2.
Hint:
1. Last digit of all the perfect square would be one of the following- 0, 1, 4, 5, 6, 9.
2. For any number ending with 0, its square would end with double the zeros at the end of that number.
3. We will use elimination method to find the correct answer.
The correct answer is: A number ending with an even number of zeros
From the given options, we know that a perfect square is obtained by multiplying a number by itself.
Hence, the last digit of all the perfect square would be one of the following- 0, 1, 4, 5, 6, 9
Hence, options b and c are eliminated.
We know that for any number ending with 0, its square would end with double the zeros at the end of that number.
Hence, option d is also eliminated.
Hence, the correct answer is option a i.e. A number ending with an even number of zeros.
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is ____
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Guess the irrational number that lies between ![10 over 14 space and space 18 over 22](data:image/png;base64,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)
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__________.
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__________.
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The square root of
![left parenthesis 7 plus 3 square root of 5 right parenthesis left parenthesis 7 minus 3 square root of 5 right parenthesis text is end text](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
Guess the irrational numbers that lies between ![4 space and space square root of 21](data:image/png;base64,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)
Guess the irrational numbers that lies between ![4 space and space square root of 21](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
What should come in place of both x in the equation
![fraction numerator x over denominator square root of 128 end fraction equals fraction numerator square root of 162 over denominator x end fraction](data:image/png;base64,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)
What should come in place of both x in the equation
![fraction numerator x over denominator square root of 128 end fraction equals fraction numerator square root of 162 over denominator x end fraction](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
Guess the smallest rational numbers among ![negative 4 over 9 comma space fraction numerator 5 over denominator negative 12 end fraction comma space fraction numerator 7 over denominator negative 18 end fraction space and space fraction numerator 2 over denominator negative 3 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMcAAAAjCAYAAAAg0B5SAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABEhJREFUeNrtXE1IVFEUvgwSQ7SJFhJDCCISIiKIRIjIQEiEyCDMIlrEIISLiGjvIiSQaBHtJFqFCCESESJERIgLIUIiJIRo0SLatBCRxyC8zvF9k9M472dG3333vnc++EBHZ+aed893zz3n/igVHyaIrjIDbgBtgpsiW+LCCHGZuEusEreIt0xq4DnitmHiSDPKxOeii0N8JN6EDzL6iBt4zQgsEKdFHFrQSVwn5kUXvugifjElrL03zCnTLI43xEHx/1A4STfgDBTaJeLQghnirPh9KK5iapUo5ol3DXRKF8kZJ2mrxAd1c1KbpwqbxA7x/UDk8ZxGkmzEQBN1mjZisyMNYbT9RrxseeJZFN8PxHnia+J40g1hdfZYNJ0Zh4PZiDIioMAf3RBGjylTF9tq8I6FnZ5D1JMk3B88I+DS9lmTG2ly5Ognfrew40sWRzwd4NL2KxtyMVPEsYKKRQ68DmFMWdj5S8SKaMAXb23JJU0RB8/Rd4gHxD8YWYYt7fzfSDTTBPeUP0u21whEHAKBiEMgMBSTyivVVzE9HfFx7jJyOQdFg0tNPmtMeTtlq/jfiohDYDMWlbe7VcGZvzYRBwvjsTraOlRRx6tqnCjzbu1+/M6fuSziEKQFOYz6jeIoRvi/F6r51nHjxeGq1hfy3DYZV/t0M6t2uBGdu/H1X6r51nrXsOcmEETGrDoqhbsnEMeBJOSCNGEB+UT+FCKHg+mWiEOQCuye4rTqgzpe6bog4vDHEh5OSewwErzJcRo/F4hzyB0KbYjjCvEd3ssRhC/h2BBxiDhsBZ/T+ay8ytMmHPyh8raxtCoORq/ytpI7EMZgVsTBCzzrMHxfeTXs7oiOdUNTG3uRYG75/P0kV7uYZAeDt2w/I+6hT9YaRvwsgUvNq/BLBwWGp5jWxQ4+PMSLQ8MImR0IxxyWOwPeN4j36dpi/JJ4J2C0avdqF9PsYPC6wiO0ic/3z2P0zyI435nCc6jvszUdX/7JJ0rUVk79UAgRT1xoJZRHudrFRDsaD3M1W5iTgoMG+NWwc5izmoZW57mmnhoMsmNP/X+RBPfFT9HDP3RjZhM7eBPZkM+ou2+5OIy42qUNOzjfuNdgxxPRxGGEryDv0JIj8vTpB5Ly2om7ibpKh63iMOJqlzbtGMCzryKX4hLsaIZF0bhN5L7OLx9D4uOAfOKuJ6bIcdI9MlHEoeNql7js4IjNu2kv1iWhQ4jwAyl09FaeG/drCYPeWJJG5A2tkIQ5nVFXu7Rhx4qPCIoYwARePpaob3JnzFkmDiuudgmxw7GwuJAEEn0WXGcvWORU1lztEmLHtk/U60PuIfAi646OL+Kb1esXWVgQvII7aZlTWXO1S4gdUxBIsa5AUkTOMZNBIXBBooxBr/YsuIB0W8eXX8Ncltc7eGFlydDELyxxs+UQTJT2sTPUqoW1c90llU2MYuCrFYvYVyeC3vAXY4DSoyVkemIAAAF4dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPi08L21vPjxtZnJhYz48bW4+NDwvbW4+PG1uPjk8L21uPjwvbWZyYWM+PG1vPiw8L21vPjxtbz4mI3hBMDs8L21vPjxtZnJhYz48bW4+NTwvbW4+PG1yb3c+PG1vPi08L21vPjxtbj4xMjwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPiw8L21vPjxtbz4mI3hBMDs8L21vPjxtZnJhYz48bW4+NzwvbW4+PG1yb3c+PG1vPi08L21vPjxtbj4xODwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPiYjeEEwOzwvbW8+PG1pPmFuZDwvbWk+PG1vPiYjeEEwOzwvbW8+PG1mcmFjPjxtbj4yPC9tbj48bXJvdz48bW8+LTwvbW8+PG1uPjM8L21uPjwvbXJvdz48L21mcmFjPjwvbWF0aD53fxI+AAAAAElFTkSuQmCC)
Guess the smallest rational numbers among ![negative 4 over 9 comma space fraction numerator 5 over denominator negative 12 end fraction comma space fraction numerator 7 over denominator negative 18 end fraction space and space fraction numerator 2 over denominator negative 3 end fraction](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
Guess the smallest rational numbers among ![4 over 9 comma space minus 5 over 6 comma space fraction numerator negative 7 over denominator negative 12 end fraction space and space fraction numerator 11 over denominator negative 24 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL4AAAAjCAYAAAAqjLAAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA/NJREFUeNrtXN9nW3EU/4qamBkzU1MzKmqqJtRUxUypmaqqUlN9qlAze9p7H6bG7D+o2dNMqamq6ctMTfShzEzVzJg9zexlDzEVEe7OkU+0XXOTm/vNzT3fe8+HDwnfJCfn+7nne77n+8OYYJgmekYuvBZ00WbJdkeJIeIK8XOX2lnhAvGLAyJKCuaJL1Iq/FfE5QD9GbSdFdaIRRV+T9BPLBGzJt3w4u73AvG9A+JKivC3iXmjiFX454gHxOsq/J7gAfJWRczCf0Z85Ii42LYqsUzcIT7G3MQVcHDZJ/ap5uMV/k3inoNRlYUzisj5lXijx50VtlLzgTiheo9f+Bx9co6nE3chKOmYxyilECD8pNSYK8Lty2Bk0gmtoBzf9QnkCPG7cBtnHRmVVPhCsUkcRwRl3oPo54R38DpxSXWuwrfJk78Ra8Q/xA3iLQc6+DfxUsLFaZti27RTKFKf+ioUKnxFcjFj6mXpKtLAgo9w5zEfqmCifa3Jd90x9Z2QVbRdUuErpOI1cRivWaiHTYTPon9ujrelLJmzVSZeBOTduSN4z9/5RoWvcAEZROv/hT8RoN1L4kKSUx0vJKP+TQn2egJpm5N7Adv9Ms23SXsp8ZvCMayY4xKvZyH8mk5uFa5gDfl7tgsRv4IUSIWvEI9yF1Od3SYVocsq/NNYh0Nm1d5YwRvfing9QFxFrj4QQvhjxHf4LEd+vnhgT4WvwpcIPk/xCRWafYj3ialvkehU+Ay+1WALaQ+LPp9k4fOiRQl/9sjUa7eDAcU0FZPNvD9nA0M9272N/yHF3nbXYhTg5zJEy+0WUxxIw/oj9HU4fIjjEELi4a0PQycPof0tPpfH5+I4QrcMoQ/h/UU4qSTI3nbXYvDiEdfMG8cmhxFhF1Iq/DD+sLoO56NPdG+s9PlhoM2DERWGYXOniMveTjqFV1UPNIsO7A+r63D8arcZ5I7SsOZYVOy0Uyqq90D+sL4Ohzcijfo8bUdCqxhXEyr8cXP24H+a4eePrlyHwynND0wMG6eapk9UCiRGAM7tN/FgVpH6LDou/CyqMgXVe1t/dO06HBb9LkRVQbUkJzTie3gopzBRzcA5vGT/MKLfs9kTEqRT+GTWFgoNSYGN31r5I/LrcBpPnDSUzenFmQa4avPTwYg/iE7OaZAP5I/Ir8PhbayrAh2zY5rvJzFCU7NWncL73/m25POq98D+iHxH5lOfyBo3OJ257+O0fYeE34+UUq8StPdHKMFzSWgOM2UDsfOK44xQB7GdvNhRPOGkMczyJx0S/lvT22sPpcPGH6GEP4mJbQ358zomEJJxBUPiX9jND8JtByZ3QYfsNMLGHy3b/AOL4dZqKWj4HwAAAXl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjQ8L21uPjxtbj45PC9tbj48L21mcmFjPjxtbz4sPC9tbz48bW8+JiN4QTA7PC9tbz48bW8+LTwvbW8+PG1mcmFjPjxtbj41PC9tbj48bW4+NjwvbW4+PC9tZnJhYz48bW8+LDwvbW8+PG1vPiYjeEEwOzwvbW8+PG1mcmFjPjxtcm93Pjxtbz4tPC9tbz48bW4+NzwvbW4+PC9tcm93Pjxtcm93Pjxtbz4tPC9tbz48bW4+MTI8L21uPjwvbXJvdz48L21mcmFjPjxtbz4mI3hBMDs8L21vPjxtaT5hbmQ8L21pPjxtbz4mI3hBMDs8L21vPjxtZnJhYz48bW4+MTE8L21uPjxtcm93Pjxtbz4tPC9tbz48bW4+MjQ8L21uPjwvbXJvdz48L21mcmFjPjwvbWF0aD6Z0DYuAAAAAElFTkSuQmCC)
Guess the smallest rational numbers among ![4 over 9 comma space minus 5 over 6 comma space fraction numerator negative 7 over denominator negative 12 end fraction space and space fraction numerator 11 over denominator negative 24 end fraction](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
How many two-digit numbers satisfy the following property given below:
The last digit (unit's digit) of the square of the two-digit number is 8?
How many two-digit numbers satisfy the following property given below:
The last digit (unit's digit) of the square of the two-digit number is 8?
MathematicsGrade-8